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Journal articles on the topic 'Cohomology with compact support'

Author: Grafiati

Published: 4 June 2021

Last updated: 18 February 2022

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1

Chatel, Gweltaz, and David Lubicz. "A Point Counting Algorithm Using Cohomology with Compact Support." LMS Journal of Computation and Mathematics 12 (2009): 295–325. http://dx.doi.org/10.1112/s1461157000001534.

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AbstractWe describe an algorithm to count the number of rational points of an hyperelliptic curve defined over a finite field of odd characteristic which is based upon the computation of the action of the Frobenius morphism on a basis of the Monsky-Washnitzer cohomology with compact support. This algorithm follows the vein of a systematic exploration of potential applications of cohomology theories to point counting.Our algorithm decomposes in two steps. A first step which consists of the computation of a basis of the cohomology and then a second step to obtain a representation of the Frobeniu

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2

García-Calcines, J. M., P. R. García-Díaz, and A. Murillo. "Brown representability for exterior cohomology and cohomology with compact supports." Journal of the London Mathematical Society 90, no. 1 (2014): 184–96. http://dx.doi.org/10.1112/jlms/jdu024.

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3

Nizioł, Wiesława. "On uniqueness of p-adic period morphisms, II." Compositio Mathematica 156, no. 9 (2020): 1915–64. http://dx.doi.org/10.1112/s0010437x20007344.

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We prove equality of the various rational $p$-adic period morphisms for smooth, not necessarily proper, schemes. We start with showing that the $K$-theoretical uniqueness criterion we had found earlier for proper smooth schemes extends to proper finite simplicial schemes in the good reduction case and to cohomology with compact support in the semistable reduction case. It yields the equality of the period morphisms for cohomology with compact support defined using the syntomic, almost étale, and motivic constructions. We continue with showing that the $h$-cohomology period morphism agrees with

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4

Yang, Wu. "On Duality for Cohomology with Compact Supports." Moscow University Mathematics Bulletin 76, no. 1 (2021): 41–43. http://dx.doi.org/10.3103/s0027132221010083.

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5

Xue, Cong. "Cuspidal cohomology of stacks of shtukas." Compositio Mathematica 156, no. 6 (2020): 1079–151. http://dx.doi.org/10.1112/s0010437x20007058.

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Let $G$ be a connected split reductive group over a finite field $\mathbb{F}_{q}$ and $X$ a smooth projective geometrically connected curve over $\mathbb{F}_{q}$. The $\ell$-adic cohomology of stacks of $G$-shtukas is a generalization of the space of automorphic forms with compact support over the function field of $X$. In this paper, we construct a constant term morphism on the cohomology of stacks of shtukas which is a generalization of the constant term morphism for automorphic forms. We also define the cuspidal cohomology which generalizes the space of cuspidal automorphic forms. Then we s

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6

V�j�itu, Viorel. "Cohomology with compact supports for cohomologically q -convex spaces." Archiv der Mathematik 80, no. 5 (2003): 496–500. http://dx.doi.org/10.1007/s00013-003-0496-7.

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7

Edmundo, Mário J., and Luca Prelli. "Invariance of o-minimal cohomology with definably compact supports." Confluentes Mathematici 7, no. 1 (2016): 35–53. http://dx.doi.org/10.5802/cml.17.

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8

Forni, Giovanni. "Homology and cohomology with compact supports forq-convex spaces." Annali di Matematica Pura ed Applicata 159, no. 1 (1991): 229–54. http://dx.doi.org/10.1007/bf01766303.

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9

Petersen, Dan. "Cohomology of generalized configuration spaces." Compositio Mathematica 156, no. 2 (2019): 251–98. http://dx.doi.org/10.1112/s0010437x19007747.

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Let $X$ be a topological space. We consider certain generalized configuration spaces of points on $X$, obtained from the cartesian product $X^{n}$ by removing some intersections of diagonals. We give a systematic framework for studying the cohomology of such spaces using what we call ‘twisted commutative dg algebra models’ for the cochains on $X$. Suppose that $X$ is a ‘nice’ topological space, $R$ is any commutative ring, $H_{c}^{\bullet }(X,R)\rightarrow H^{\bullet }(X,R)$ is the zero map, and that $H_{c}^{\bullet }(X,R)$ is a projective $R$-module. We prove that the compact support cohomolo

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10

CHAPOTON, F. "ON THE NUMBER OF POINTS OVER FINITE FIELDS ON VARIETIES RELATED TO CLUSTER ALGEBRAS." Glasgow Mathematical Journal 53, no. 1 (2010): 141–51. http://dx.doi.org/10.1017/s0017089510000777.

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AbstractWe start here the study of some algebraic varieties related to cluster algebras. These varieties are defined as the fibres of the projection map from the cluster variety to the affine space of coefficients. We compute the number of points over finite fields on these varieties, for all simply laced Dynkin diagrams. We also compute the cohomology with compact support in some cases.

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11

Bondarko, Mikhail V., and David Z. Kumallagov. "On Chow-weight homology of motivic complexes and its relation to motivic homology." Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy 65, no. 4 (2020): 560–87. http://dx.doi.org/10.21638/spbu01.2020.401.

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In this paper we study in detail the so-called Chow-weight homology of Voevodsky motivic complexes and relate it to motivic homology. We generalize earlier results and prove that the vanishing of higher motivic homology groups of a motif M implies similar vanishing for its Chow-weight homology along with effectivity properties of the higher terms of its weight complex t(M) and of higher Deligne weight quotients of its cohomology. Applying this statement to motives with compact support we obtain a similar relation between the vanishing of Chow groups and the cohomology with compact support of v

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12

Leal, Isabel. "On the ramification of étale cohomology groups." Journal für die reine und angewandte Mathematik (Crelles Journal) 2019, no. 749 (2019): 295–304. http://dx.doi.org/10.1515/crelle-2016-0035.

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Abstract Let K be a complete discrete valuation field whose residue field is perfect and of positive characteristic, let X be a connected, proper scheme over \mathcal{O}_{K} , and let U be the complement in X of a divisor with simple normal crossings. Assume that the pair (X,U) is strictly semi-stable over \mathcal{O}_{K} of relative dimension one and K is of equal characteristic. We prove that, for any smooth \ell -adic sheaf \mathcal{G} on U of rank one, at most tamely ramified on the generic fiber, if the ramification of \mathcal{G} is bounded by t+ for the logarithmic upper ramification gr

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13

Chojecki, Przemysław. "On non-abelian Lubin–Tate theory for." Compositio Mathematica 151, no. 8 (2015): 1433–61. http://dx.doi.org/10.1112/s0010437x14008008.

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We analyse the$\text{mod}~p$étale cohomology of the Lubin–Tate tower both with compact support and without support. We prove that there are no supersingular representations in the$H_{c}^{1}$of the Lubin–Tate tower. On the other hand, we show that in$H^{1}$of the Lubin–Tate tower appears the$\text{mod}~p$local Langlands correspondence and the$\text{mod}~p$local Jacquet–Langlands correspondence, which we define in the text. We discuss the local-global compatibility part of the Buzzard–Diamond–Jarvis conjecture which appears naturally in this context.

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14

Tomassini, Giuseppe, and Viorel Vâjâitu. "On the cohomology with compact supports for q-complete mixed manifolds." Annali di Matematica Pura ed Applicata 181, no. 4 (2002): 349–63. http://dx.doi.org/10.1007/s102310100035.

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15

Dimca, Alexandru, and Morihiko Saito. "Number of Jordan blocks of the maximal size for local monodromies." Compositio Mathematica 150, no. 3 (2014): 344–68. http://dx.doi.org/10.1112/s0010437x13007513.

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AbstractWe prove formulas for the number of Jordan blocks of the maximal size for local monodromies of one-parameter degenerations of complex algebraic varieties where the bound of the size comes from the monodromy theorem. In the case when the general fibers are smooth and compact, the proof calculates some part of the weight spectral sequence of the limit mixed Hodge structure of Steenbrink. In the singular case, we can prove a similar formula for the monodromy on the cohomology with compact supports, but not on the usual cohomology. We also show that the number can really depend on the posi

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16

Yang, Yaping, and Gufang Zhao. "On two cohomological Hall algebras." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 150, no. 3 (2019): 1581–607. http://dx.doi.org/10.1017/prm.2018.162.

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AbstractWe compare two cohomological Hall algebras (CoHA). The first one is the preprojective CoHA introduced in [19] associated with each quiver Q, and each algebraic oriented cohomology theory A. It is defined as the A-homology of the moduli of representations of the preprojective algebra of Q, generalizing the K-theoretic Hall algebra of commuting varieties of Schiffmann-Vasserot [15]. The other one is the critical CoHA defined by Kontsevich-Soibelman associated with each quiver with potentials. It is defined using the equivariant cohomology with compact support with coefficients in the she

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17

Beraldo, Dario. "Tempered D-modules and Borel–Moore homology vanishing." Inventiones mathematicae 225, no. 2 (2021): 453–528. http://dx.doi.org/10.1007/s00222-021-01036-2.

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AbstractWe characterize the tempered part of the automorphic Langlands category $$\mathfrak {D}({\text {Bun}}_G)$$ D ( Bun G ) using the geometry of the big cell in the affine Grassmannian. We deduce that, for G non-abelian, tempered D-modules have no de Rham cohomology with compact support. The latter fact boils down to a concrete statement, which we prove using the Ran space and some explicit t-structure estimates: for G non-abelian and $$\Sigma $$ Σ a smooth affine curve, the Borel–Moore homology of the indscheme $${\text {Maps}}(\Sigma ,G)$$ Maps ( Σ , G ) vanishes.

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18

Morel, Sophie. "Cohomologie d’intersection des variétés modulaires de Siegel, suite." Compositio Mathematica 147, no. 6 (2011): 1671–740. http://dx.doi.org/10.1112/s0010437x11005409.

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AbstractIn this work, we study the intersection cohomology of Siegel modular varieties. The goal is to express the trace of a Hecke operator composed with a power of the Frobenius endomorphism (at a good place) on this cohomology in terms of the geometric side of Arthur’s invariant trace formula for well-chosen test functions. Our main tools are the results of Kottwitz about the contribution of the cohomology with compact support and about the stabilization of the trace formula, Arthur’s L2 trace formula and the fixed point formula of Morel [Complexes pondérés sur les compactifications de Bail

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19

SEKIGUCHI, HIDEKO. "BRANCHING RULES OF SINGULAR UNITARY REPRESENTATIONS WITH RESPECT TO SYMMETRIC PAIRS (A2n-1, Dn)." International Journal of Mathematics 24, no. 04 (2013): 1350011. http://dx.doi.org/10.1142/s0129167x13500110.

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The irreducible decomposition of scalar holomorphic discrete series representations when restricted to semisimple symmetric pairs (G, H) is explicitly known by Schmid [Die Randwerte holomorphe funktionen auf hermetisch symmetrischen Raumen, Invent. Math.9 (1969–1970) 61–80] for H compact and by Kobayashi [Multiplicity-Free Theorems of the Restrictions of Unitary Highest Weight Modules with Respect to Reductive Symmetric Pairs, Progress in Mathematics, Vol. 255 (Birhäuser, 2007), pp. 45–109] for H non-compact. In this paper, we deal with the symmetric pair (U(n, n), SO* (2n)), and extend the Ko

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20

ALBIN, PIERRE, and RICHARD MELROSE. "RELATIVE CHERN CHARACTER, BOUNDARIES AND INDEX FORMULAS." Journal of Topology and Analysis 01, no. 03 (2009): 207–50. http://dx.doi.org/10.1142/s1793525309000151.

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For three classes of elliptic pseudodifferential operators on a compact manifold with boundary which have "geometric K-theory", namely the "transmission algebra" introduced by Boutet de Monvel [5], the "zero algebra" introduced by Mazzeo in [9, 10] and the "scattering algebra" from [16], we give explicit formulas for the Chern character of the index bundle in terms of the symbols (including normal operators at the boundary) of a Fredholm family of fiber operators. This involves appropriate descriptions, in each case, of the cohomology with compact supports in the interior of the total space of

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21

Papadima, Stefan, and Alexander I. Suciu. "The Topology of Compact Lie Group Actions Through the Lens of Finite Models." International Mathematics Research Notices 2019, no. 20 (2018): 6390–436. http://dx.doi.org/10.1093/imrn/rnx294.

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AbstractGiven a compact, connected Lie group K, we use principal K-bundles to construct manifolds with prescribed finite-dimensional algebraic models. Conversely, let M be a compact, connected, smooth manifold, which supports an almost free K-action. Under a partial formality assumption on the orbit space and a regularity assumption on the characteristic classes of the action, we describe an algebraic model for M with commensurate finiteness and partial formality properties. The existence of such a model has various implications on the structure of the cohomology jump loci of M and of the repr

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22

Haines, Thomas J. "On Connected Components of Shimura Varieties." Canadian Journal of Mathematics 54, no. 2 (2002): 352–95. http://dx.doi.org/10.4153/cjm-2002-012-x.

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AbstractWe study the cohomology of connected components of Shimura varieties coming from the group GSp2g, by an approach modeled on the stabilization of the twisted trace formula, due to Kottwitz and Shelstad. More precisely, for each character ϖ on the group of connected components of we define an operator L(ω) on the cohomology groups with compact supports Hic(, ), and then we prove that the virtual trace of the composition of L(ω) with a Hecke operator f away from p and a sufficiently high power of a geometric Frobenius , can be expressed as a sum of ω-weighted (twisted) orbital integrals (

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23

Rajhi, Anis. "Cohomologie à support compact d’un espace au-dessus de l’immeuble de Bruhat-Tits de GL n sur un corps local. Représentations cuspidales de niveau zéro." Confluentes Mathematici 10, no. 1 (2018): 95–124. http://dx.doi.org/10.5802/cml.47.

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24

Console, S., and A. Fino. "Dolbeault cohomology of compact nilmanifolds." Transformation Groups 6, no. 2 (2001): 111–24. http://dx.doi.org/10.1007/bf01597131.

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25

Trapani, Stefano. "Holomorphically convex compact sets and cohomology." Pacific Journal of Mathematics 134, no. 1 (1988): 179–96. http://dx.doi.org/10.2140/pjm.1988.134.179.

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26

Gorbatsevich, V. V. "Stable cohomology of compact homogeneous spaces." Mathematical Notes 83, no. 5-6 (2008): 735–43. http://dx.doi.org/10.1134/s0001434608050192.

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27

BISWAS, INDRANIL, and PRALAY CHATTERJEE. "SECOND COHOMOLOGY OF COMPACT HOMOGENEOUS SPACES." International Journal of Mathematics 24, no. 09 (2013): 1350076. http://dx.doi.org/10.1142/s0129167x13500766.

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In Theorem 3.3 of [I. Biswas and P. Chatterjee, On the exactness of Kostant–Kirillov form and the second cohomology of nilpotent orbits, Int. J. Math.23(8) (2012)], the second cohomology of a quotient of a compact semisimple real Lie group was computed. In this addendum to the above paper, we give a simple topological proof of this theorem.

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28

Andersen, Kasper K. S., Natàlia Castellana, Vincent Franjou, Alain Jeanneret, and Jérôme Scherer. "Spaces with Noetherian cohomology." Proceedings of the Edinburgh Mathematical Society 56, no. 1 (2012): 13–25. http://dx.doi.org/10.1017/s0013091512000193.

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AbstractIs the cohomology of the classifying space of a p-compact group, with Noetherian twisted coefficients, a Noetherian module? In this paper we provide, over the ring of p-adic integers, such a generalization to p-compact groups of the Evens–Venkov Theorem. We consider the cohomology of a space with coefficients in a module, and we compare Noetherianity over the field with p elements with Noetherianity over the p-adic integers, in the case when the fundamental group is a finite p-group.

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29

GINZBURG, VIKTOR L. "MOMENTUM MAPPINGS AND POISSON COHOMOLOGY." International Journal of Mathematics 07, no. 03 (1996): 329–58. http://dx.doi.org/10.1142/s0129167x96000207.

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We analyze the question of existence and uniqueness of equivariant momentum mappings for Poisson actions of Poisson Lie groups. A necessary and sufficient condition for the equivariant momentum mapping to be unique is given. The existence problem is solved under some extra hypotheses, for example, when the action preserves the Poisson structure. In this case, the problem is closely related to the triviality of the induced group action on the Poisson cohomology. This action is shown to be trivial whenever the group is compact or semisimple. Conceptually, these results rely upon a version of “Po

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30

Lowen, Wendy. "Hochschild Cohomology with Support." International Mathematics Research Notices 2015, no. 13 (2014): 4741–812. http://dx.doi.org/10.1093/imrn/rnu079.

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31

Ramani, Vimala, and Parameswaran Sankaran. "Dolbeault cohomology of compact complex homogeneous manifolds." Proceedings Mathematical Sciences 109, no. 1 (1999): 11–21. http://dx.doi.org/10.1007/bf02837763.

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32

Zhang, Dong, Bohui Chen, and Cheng-Yong Du. "A quantum modification of relative cohomology." International Journal of Geometric Methods in Modern Physics 12, no. 02 (2015): 1550021. http://dx.doi.org/10.1142/s0219887815500218.

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In this paper, we give a quantum modification of the relative cup product on H*(X, S;ℝ) by using Gromov–Witten invariants when S is a compact codimension 2k symplectic submanifold of the compact symplectic manifold (X, ω).

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33

LÉANDRE, RÉMI. "STOCHASTIC ADAMS THEOREM FOR A GENERAL COMPACT MANIFOLD." Reviews in Mathematical Physics 13, no. 09 (2001): 1095–133. http://dx.doi.org/10.1142/s0129055x01000909.

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We give a stochastic analoguous of the theorem of Adams, which says that the Hochschild cohomology is equal to the cohomology of the based smooth loop space. The key tools are the stochastic Chen iterated integrals as well as Driver's flow.

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34

Bytsenko, A. A., M. Libine, and F. L. Williams. "Localization of Equivariant Cohomology for Compact and Non-Compact Group Actions." Journal of Dynamical Systems and Geometric Theories 3, no. 2 (2005): 171–95. http://dx.doi.org/10.1080/1726037x.2005.10698497.

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35

DEY, PINKA, and MAHENDER SINGH. "FREE ACTIONS OF SOME COMPACT GROUPS ON MILNOR MANIFOLDS." Glasgow Mathematical Journal 61, no. 03 (2018): 727–42. http://dx.doi.org/10.1017/s0017089518000484.

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AbstractIn this paper, we investigate free actions of some compact groups on cohomology real and complex Milnor manifolds. More precisely, we compute the mod 2 cohomology algebra of the orbit space of an arbitrary free ℤ2 and $\mathbb{S}^1$-action on a compact Hausdorff space with mod 2 cohomology algebra of a real or a complex Milnor manifold. As applications, we deduce some Borsuk–Ulam type results for equivariant maps between spheres and these spaces. For the complex case, we obtain a lower bound on the Schwarz genus, which further establishes the existence of coincidence points for maps to

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36

BRODZKI, JACEK, GRAHAM A. NIBLO, PIOTR W. NOWAK, and NICK WRIGHT. "AMENABLE ACTIONS, INVARIANT MEANS AND BOUNDED COHOMOLOGY." Journal of Topology and Analysis 04, no. 03 (2012): 321–34. http://dx.doi.org/10.1142/s1793525312500161.

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We show that amenability of an action of a discrete group on a compact space X is equivalent to vanishing of bounded cohomology for a class of Banach G-modules associated to the action, that can be viewed as analogs of continuous bundles of dual modules over the G-space X. In the case when the compact space is a point, our result reduces to a classic theorem of Johnson, characterising amenability of groups. In the case when the compact space is the Stone–Čech compactification of the group, we obtain a cohomological characterisation of exactness, or equivalently, Yu's property A for the group,

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37

NESHVEYEV, SERGEY, and LARS TUSET. "ON SECOND COHOMOLOGY OF DUALS OF COMPACT GROUPS." International Journal of Mathematics 22, no. 09 (2011): 1231–60. http://dx.doi.org/10.1142/s0129167x11007239.

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We show that for any compact connected group G the second cohomology group defined by unitary invariant two-cocycles on Ĝ is canonically isomorphic to [Formula: see text]. This implies that the group of autoequivalences of the C*-tensor category Rep G is isomorphic to [Formula: see text]. We also show that a compact connected group G is completely determined by Rep G. More generally, extending a result of Etingof–Gelaki and Izumi–Kosaki we describe all pairs of compact separable monoidally equivalent groups. The proofs rely on the theory of ergodic actions of compact groups developed by Landst

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38

Budur, Nero, and Botong Wang. "Cohomology jump loci of quasi-compact Kähler manifolds." Pure and Applied Mathematics Quarterly 16, no. 4 (2020): 981–99. http://dx.doi.org/10.4310/pamq.2020.v16.n4.a3.

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39

Cordero, Luis A., Marisa Fernández, Alfred Gray, and Luis Ugarte. "Compact nilmanifolds with nilpotent complex structures: Dolbeault cohomology." Transactions of the American Mathematical Society 352, no. 12 (2000): 5405–33. http://dx.doi.org/10.1090/s0002-9947-00-02486-7.

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40

Guan, Daniel. "Modification and the cohomology groups of compact solvmanifolds." Electronic Research Announcements of the American Mathematical Society 13, no. 08 (2007): 74–82. http://dx.doi.org/10.1090/s1079-6762-07-00176-x.

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41

Mazzeo, Rafe. "The Hodge cohomology of a conformally compact metric." Journal of Differential Geometry 28, no. 2 (1988): 309–39. http://dx.doi.org/10.4310/jdg/1214442281.

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42

Brudnyi, A. Yu, and A. L. Onishchik. "Triangular de Rham cohomology of compact Kahler manifolds." Sbornik: Mathematics 192, no. 2 (2001): 187–214. http://dx.doi.org/10.1070/sm2001v192n02abeh000541.

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43

Angella, Daniele, Georges Dloussky, and Adriano Tomassini. "On Bott-Chern cohomology of compact complex surfaces." Annali di Matematica Pura ed Applicata (1923 -) 195, no. 1 (2014): 199–217. http://dx.doi.org/10.1007/s10231-014-0458-7.

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44

Ancona, Vincenzo, and Bernard Gaveau. "Holomorphic cohomology groups on compact Kähler complex spaces." Bulletin des Sciences Mathématiques 134, no. 7 (2010): 705–23. http://dx.doi.org/10.1016/j.bulsci.2010.06.004.

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45

Verbitsky, Mikhail. "Cohomology of compact hyperkähler manifolds and its applications." Geometric and Functional Analysis 6, no. 4 (1996): 601–11. http://dx.doi.org/10.1007/bf02247112.

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46

Hebda, James J. "The possible cohomology of certain types of taut submanifolds." Nagoya Mathematical Journal 111 (September 1988): 85–97. http://dx.doi.org/10.1017/s0027763000001008.

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The first purpose of this paper is to exhibit several families of compact manifolds that do not ad nit taut embeddings into any sphere. The second is to enumerate ths possible Z2-cohomology rings of those compact manifolds which do admit a taut embedding and whose cohomology rings satisfy certain degeneracy conditions. The first purpose is easily attained once the second has been accomplished, for it is a simple matter to present families of spaces whose cohomology rings satisfy the required degeneracy conditions, but are not on the list of those admitting a taut embedding.

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47

Hirsch, Morris W., and Charles C. Pugh. "Cohomology of chain recurrent sets." Ergodic Theory and Dynamical Systems 8, no. 1 (1988): 73–80. http://dx.doi.org/10.1017/s0143385700004326.

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AbstractLet ϕ be a flow on a compact metric space Λ and let p ∈ Λ be chain recurrent. We show that (Λ; ℝ) ≠ 0 if dimp Λ = 1 or if p belongs to a section of ϕ. Applications to planar flows and to smooth flows are given.

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48

Kuhn, Nicholas J. "Nilpotence in group cohomology." Proceedings of the Edinburgh Mathematical Society 56, no. 1 (2012): 151–75. http://dx.doi.org/10.1017/s001309151200017x.

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AbstractWe study bounds on nilpotence in H*(BG), the mod p cohomology of the classifying space of a compact Lie group G. Part of this is a report of our previous work on this problem, updated to reflect the consequences of Peter Symonds's recent verification of Dave Benson's Regularity Conjecture. New results are given for finite p-groups, leading to good bounds on nilpotence in H*(BP) determined by the subgroup structure of the p-group P.

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49

Berarducci, Alessandro. "O-minimal spectra, infinitesimal subgroups and cohomology." Journal of Symbolic Logic 72, no. 4 (2007): 1177–93. http://dx.doi.org/10.2178/jsl/1203350779.

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AbstractBy recent work on some conjectures of Pillay, each definably compact group G in a saturated o-minimal expansion of an ordered field has a normal “infinitesimal subgroup” G00 such that the quotient G/G00, equipped with the “logic topology”, is a compact (real) Lie group. Our first result is that the functor G ↦ G/G00 sends exact sequences of definably compact groups into exact sequences of Lie groups. We then study the connections between the Lie group G/G00 and the o-minimal spectrum of G. We prove that G/G00 is a topological quotient of . We thus obtain a natural homomorphism Ψ* from

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BERARDUCCI, ALESSANDRO, and ANTONGIULIO FORNASIERO. "o-MINIMAL COHOMOLOGY: FINITENESS AND INVARIANCE RESULTS." Journal of Mathematical Logic 09, no. 02 (2009): 167–82. http://dx.doi.org/10.1142/s0219061309000859.

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Abstract:

The topology of definable sets in an o-minimal expansion of a group is not fully understood due to the lack of a triangulation theorem. Despite the general validity of the cell decomposition theorem, we do not know whether any definably compact set is a definable CW-complex. Moreover the closure of an o-minimal cell can have arbitrarily high Betti numbers. Nevertheless we prove that the cohomology groups of a definably compact set over an o-minimal expansion of a group are finitely generated and invariant under elementary extensions and expansions of the language.

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