Relevant bibliographies by topics / Torus bundle group

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  2. Dissertations / Theses
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Academic literature on the topic 'Torus bundle group'

Author: Grafiati
Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Torus bundle group"

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Bunke, Ulrich, and Thomas Nikolaus. "T-duality via gerby geometry and reductions." Reviews in Mathematical Physics 27, no. 05 (2015): 1550013. http://dx.doi.org/10.1142/s0129055x15500130.

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We consider topological T-duality of torus bundles equipped with [Formula: see text]-gerbes. We show how a geometry on the gerbe determines a reduction of its band to the subsheaf of S1-valued functions which are constant along the torus fibers. We observe that such a reduction is exactly the additional datum needed for the construction of a T-dual pair. We illustrate the theory by working out the example of the canonical lifting gerbe on a compact Lie group which is a torus bundle over the associated flag manifold. It was a recent observation of Daenzer and van Erp [16] that for certain compact Lie groups and a particular choice of the gerbe, the T-dual torus bundle is given by the Langlands dual group.
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GASHI, QËNDRIM R., and TRAVIS SCHEDLER. "NORMALITY AND QUADRATICITY FOR SPECIAL AMPLE LINE BUNDLES ON TORIC VARIETIES ARISING FROM ROOT SYSTEMS." Glasgow Mathematical Journal 55, A (2013): 113–34. http://dx.doi.org/10.1017/s0017089513000542.

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AbstractWe prove that special ample line bundles on toric varieties arising from root systems are projectively normal. Here the maximal cones of the fans correspond to the Weyl chambers, and special means that the bundle is torus-equivariant such that the character of the line bundle that corresponds to a maximal Weyl chamber is dominant with respect to that chamber. Moreover, we prove that the associated semi-group rings are quadratic.
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Poddar, Mainak, and Ajay Singh Thakur. "Group actions, non-Kähler complex manifolds and SKT structures." Complex Manifolds 5, no. 1 (2018): 9–25. http://dx.doi.org/10.1515/coma-2018-0002.

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AbstractWe give a construction of integrable complex structures on the total space of a smooth principal bundle over a complex manifold, with an even dimensional compact Lie group as structure group, under certain conditions. This generalizes the constructions of complex structure on compact Lie groups by Samelson and Wang, and on principal torus bundles by Calabi-Eckmann and others. It also yields large classes of new examples of non-Kähler compact complex manifolds. Moreover, under suitable restrictions on the base manifold, the structure group, and characteristic classes, the total space of the principal bundle admits SKT metrics. This generalizes recent results of Grantcharov et al. We study the Picard group and the algebraic dimension of the total space in some cases. We also use a slightly generalized version of the construction to obtain (non-Kähler) complex structures on tangential frame bundles of complex orbifolds.
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Lee, Min Ho. "Existence of Torus bundles associated to cocycles." Bulletin of the Australian Mathematical Society 73, no. 3 (2006): 345–51. http://dx.doi.org/10.1017/s0004972700035383.

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A Kuga fibre variety is a fibre bundle over a locally symmetric space whose fibre is a polarized Abelian variety. We describe a complex torus bundle associated to a 2-cocycle of a discrete group, which may be regarded as a generalized Kuga fibre variety, and prove the existence of such a bundle.
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Florentino, Carlos, and Thomas Ludsteck. "Unipotent Schottky bundles on Riemann surfaces and complex tori." International Journal of Mathematics 25, no. 06 (2014): 1450056. http://dx.doi.org/10.1142/s0129167x14500566.

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We study a natural map from representations of a free (respectively, free abelian) group of rank g in GL r(ℂ), to holomorphic vector bundles of degree zero over a compact Riemann surface X of genus g (respectively, complex torus X of dimension g). This map defines what is called a Schottky functor. Our main result is that this functor induces an equivalence between the category of unipotent representations of Schottky groups and the category of unipotent vector bundles on X. We also show that, over a complex torus, any vector or principal bundle with a flat holomorphic connection is Schottky.
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Biswas, Indranil, Arijit Dey, and Mainak Poddar. "A classification of equivariant principal bundles over nonsingular toric varieties." International Journal of Mathematics 27, no. 14 (2016): 1650115. http://dx.doi.org/10.1142/s0129167x16501159.

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We classify holomorphic as well as algebraic torus equivariant principal [Formula: see text]-bundles over a nonsingular toric variety [Formula: see text], where [Formula: see text] is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric variety admits a trivialization in equivariant sense. We also obtain some splitting results.
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BISWAS, INDRANIL. "HOLOMORPHIC PRINCIPAL BUNDLES WITH AN ELLIPTIC CURVE AS THE STRUCTURE GROUP." International Journal of Geometric Methods in Modern Physics 05, no. 06 (2008): 851–62. http://dx.doi.org/10.1142/s0219887808003004.

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Let Λ ⊂ ℂ be the ℤ-module generated by 1 and [Formula: see text], where τ is a positive real number. Let Z := ℂ/Λ be the corresponding complex torus of dimension one. Our aim here is to give a general construction of holomorphic principal Z-bundles over a complex manifold X. Let θ1 and θ2 be two C∞ real closed two-forms on X such that the Hodge type (0, 2) component of the form [Formula: see text] vanishes, and the elements in H2(X, ℂ) represented by θ1 and θ2 are contained in the image of H2(X, ℤ). For such a pair we construct a holomorphic principal Z-bundle over X. Conversely, given any holomorphic principal Z-bundle EZ over X, we construct a pair of closed differential forms on X of the above type.
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Abe, Yukitaka. "Homogeneous line bundles over a toroidal group." Nagoya Mathematical Journal 116 (December 1989): 17–24. http://dx.doi.org/10.1017/s0027763000001665.

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A connected complex Lie group without non-constant holomorphic functions is called a toroidal group ([5]) or an (H, C)-group ([9]). Let X be an n-dimensional toroidal group. Since a toroidal group is commutative ([5], [9] and [10]), X is isomorphic to the quotient group Cn/Γ by a lattice of Cn. A complex torus is a compact toroidal group. Cousin first studied a non-compact toroidal group ([2]).Let L be a holomorphic line bundle over X. L is said to be homogeneous if is isomorphic to L for all x ε X, where Tx is the translation defined by x ε X. It is well-known that if X is a complex torus, then the following assertions are equivalent:
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Mangum, Brian, and Patrick Shanahan. "Three-Dimensional Representations of Punctured Torus Bundles." Journal of Knot Theory and Its Ramifications 06, no. 06 (1997): 817–25. http://dx.doi.org/10.1142/s0218216597000455.

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In this paper, we construct a complex curve of irreducible [Formula: see text] representations of the fundamental group of a once punctured torus bundle over the circle. These representations are different from those obtained by composing representations in [Formula: see text] with the unique irreducible representation of [Formula: see text] in [Formula: see text]. Moreover, infinitely many of these representations are conjugate to SU(3) representations. We conclude the paper with a computation of the curve in the case that the bundle is the figure-eight knot complement, and we show that for infinitely many Dehn surgeries on the figure-eight knot, there is a representation from this curve that descends to a representation of the fundamental group of the surgered manifold.
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LEVINE, MARC. "MOTIVIC EULER CHARACTERISTICS AND WITT-VALUED CHARACTERISTIC CLASSES." Nagoya Mathematical Journal 236 (March 22, 2019): 251–310. http://dx.doi.org/10.1017/nmj.2019.6.

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This paper examines Euler characteristics and characteristic classes in the motivic setting. We establish a motivic version of the Becker–Gottlieb transfer, generalizing a construction of Hoyois. Making calculations of the Euler characteristic of the scheme of maximal tori in a reductive group, we prove a generalized splitting principle for the reduction from $\operatorname{GL}_{n}$ or $\operatorname{SL}_{n}$ to the normalizer of a maximal torus (in characteristic zero). Ananyevskiy’s splitting principle reduces questions about characteristic classes of vector bundles in $\operatorname{SL}$-oriented, $\unicode[STIX]{x1D702}$-invertible theories to the case of rank two bundles. We refine the torus-normalizer splitting principle for $\operatorname{SL}_{2}$ to help compute the characteristic classes in Witt cohomology of symmetric powers of a rank two bundle, and then generalize this to develop a general calculus of characteristic classes with values in Witt cohomology.
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Dissertations / Theses on the topic "Torus bundle group"

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Martins, Sergio Tadao. "Aproximações da diagonal e anéis de cohomologia dos grupos fundamentais das superfícies, de fibrados do toro e de certos grupos virtualmente cíclicos." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/45/45131/tde-25022013-105446/.

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Dado um grupo G, a definição dos grupos de cohomologia com coeficientes em um ZG-módulo M podem ser dadas usando as técnicas usuais da Álgebra Homológica, que garantem a existência de resoluções projetivas P de Z como um ZG-módulo trivial, a equivalência entre resoluções distintas etc. Podemos também construir o produto cup em cohomologia, cuja definição depende de uma aproximação da diagonal para a resolução projetiva P. Entretanto, o cálculo explicito de tais resoluções e dos grupos de cohomologia pode ser bastante difícil na prática, e ainda mais difícil a obtenção de uma aproximação da diagonal. Nesta tese, obteremos resoluções livres e aproximações da diagonal para os grupos fundamentais das superfícies que são espaços K(G,1) e também para o grupo fundamental de fibrados do toro com base S^1, bem como a estrutura de anel de cohomologia de tais grupos. Ainda, para certos grupos virtualmente cíclicos G, obteremos o anel de cohomologia calculando diretamente uma resolução livre e uma aproximação da diagonal, ou então usando a sequência espectral de Lyndon-Hochschild-Serre. A motivação para o estudo da primeira família de grupos vem do fato de representarem variedades de dimensão 2 e 3, e da segunda família por ser constituída de grupos que atuam em esferas de homotopia.<br>Given a group G, a definition for its cohomology groups with coefficients in a given ZG-module M can be given using the standard techniques of Homological Algebra, that ensure the existence of projective resolutions P of Z as a trivial ZG-module, the equivalence between two such resolutions etc . We can also construct the cup product, whose definition depends on a diagonal approximation for a given projective resolution P. However, the explicit computation of such resolutions and of the cohomology groups may be very hard in practice, and even worse may be the task of constructing a diagonal approximation. In this thesis, we obtain free resolutions and diagonal approximations for the fundamental groups of surfaces that are K(G,1) spaces and for the fundamental group of the torus bundle with the circle as the base space, as well as the structure of the cohomology ring of these groups. Also, for some virtually cyclic groups, we obtain the cohomology ring by an explicit computation of a free resolution and a diagonal approximation, or by the Lyndon-Hochschild-Serre spectral sequence. The motivation for the study of the first family of groups comes from the fact that such groups represent manifolds of dimension 2 and 3, and the groups of the second family act on homotopy spheres.
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Ascah-Coallier, Isabelle. "Le théorème de Borel-Weil-Bott." Thèse, 2008. http://hdl.handle.net/1866/7875.

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Books on the topic "Torus bundle group"

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McDuff, Dusa, and Dietmar Salamon. Symplectic group actions. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198794899.003.0006.

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The chapter begins with a discussion of circle actions and their relation to 2-sphere bundles. It continues with a section on general Hamiltonian group actions and moment maps, then proceeds to discuss various explicit examples in both finite and infinite dimensions, and introduces the Marsden–Weinstein quotient, together with new examples that explain its relation to the construction of generating functions for Lagrangians. Further sections give a proof of the Atiyah–Guillemin–Sternberg convexity theorem about the image of the moment map in the case of torus actions, and use equivariant cohomology to prove the Duistermaat–Heckman localization formula for circle actions. It closes with an overview of geometric invariant theory which grows out of the interplay between the actions of a real Lie group and its complexification.
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Book chapters on the topic "Torus bundle group"

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Berdinsky, Dmitry, and Prohrak Kruengthomya. "Nonstandard Cayley Automatic Representations for Fundamental Groups of Torus Bundles over the Circle." In Language and Automata Theory and Applications. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-40608-0_7.

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MATSUSHIMA, Yozo. "ON THE INTERMEDIATE COHOMOLOGY GROUP OF A HOLOMORPHIC LINE BUNDLE OVER A COMPLEX TORUS." In Collected Papers of Y Matsushima. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814360067_0047.

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Parker, J. R. "Tetrahedral decomposition of punctured torus bundles." In Kleinian Groups and Hyperbolic 3-Manifolds. Cambridge University Press, 2003. http://dx.doi.org/10.1017/cbo9780511542817.013.

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MATSUSHIMA, YOZO. "HEISENBERG GROUPS AND HOLOMORPHIC VECTOR BUNDLES OVER A COMPLEX TORUS." In Collected Papers of Y Matsushima. WORLD SCIENTIFIC, 1992. http://dx.doi.org/10.1142/9789814360067_0046.

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