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Relevant bibliographies by topics / First Cohomology Group

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Academic literature on the topic 'First Cohomology Group'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "First Cohomology Group"

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Puls, Michael J. "Group Cohomology and Lp-Cohomology of Finitely Generated Groups." Canadian Mathematical Bulletin 46, no. 2 (2003): 268–76. http://dx.doi.org/10.4153/cmb-2003-027-x.

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AbstractLet G be a finitely generated, infinite group, let p > 1, and let Lp(G) denote the Banach space . In this paper we will study the first cohomology group of G with coefficients in Lp(G), and the first reduced Lp-cohomology space of G. Most of our results will be for a class of groups that contains all finitely generated, infinite nilpotent groups.

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Satoh, Takao. "On the low-dimensional cohomology groups of the IA-automorphism group of the free group of rank three." Proceedings of the Edinburgh Mathematical Society 64, no. 2 (2021): 338–63. http://dx.doi.org/10.1017/s0013091521000171.

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AbstractIn this paper, we study the structure of the rational cohomology groups of the IA-automorphism group $\mathrm {IA}_3$ of the free group of rank three by using combinatorial group theory and representation theory. In particular, we detect a nontrivial irreducible component in the second cohomology group of $\mathrm {IA}_3$, which is not contained in the image of the cup product map of the first cohomology groups. We also show that the triple cup product of the first cohomology groups is trivial. As a corollary, we obtain that the fourth term of the lower central series of $\mathrm {IA}_

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Manea, Adelina. "First and second cohomology group of a bu ndle." Analele Universitatii "Ovidius" Constanta - Seria Matematica 20, no. 2 (2012): 71–78. http://dx.doi.org/10.2478/v10309-012-0041-4.

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Abstract Let (E, π, M) be a vector bundle. We define two cohomology groups associated to π using the first and second order jet manifolds of this bundle. We prove that one of them is isomorphic with a Čech cohomology group of the base space. The particular case of trivial bundle is studied

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Komy, S. R. "On the first cohomology group for simply connected Lie groups." Journal of Physics A: Mathematical and General 18, no. 8 (1985): 1159–65. http://dx.doi.org/10.1088/0305-4470/18/8/016.

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Medghalchi, A. R., and H. Pourmahmood-Aghababa. "The first cohomology group of module extension Banach algebras." Rocky Mountain Journal of Mathematics 41, no. 5 (2011): 1639–51. http://dx.doi.org/10.1216/rmj-2011-41-5-1639.

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de la Pe�a, Jos� Antonio, and Manuel Saor�n. "On the first Hochschild cohomology group of an algebra." manuscripta mathematica 104, no. 4 (2001): 431–42. http://dx.doi.org/10.1007/s002290170017.

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Hazrat, R. "On the First Galois Cohomology Group of the Algebraic Group SL1(D)." Communications in Algebra 36, no. 2 (2008): 381–87. http://dx.doi.org/10.1080/00927870701715696.

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Koam, Ali. "Oriented Algebras and the Hochschild Cohomology Group." Mathematics 6, no. 11 (2018): 237. http://dx.doi.org/10.3390/math6110237.

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Koam and Pirashivili developed the equivariant version of Hochschild cohomology by mixing the standard chain complexes computing group with associative algebra cohomologies to obtain the bicomplex C ˜ G * ( A , X ). In this paper, we form a new bicomplex F ˘ G * ( A , X ) by deleting the first column and the first row and reindexing. We show that H ˘ G 1 ( A , X ) classifies the singular extensions of oriented algebras.

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Liu, Wende, and Yong Yang. "Cohomology of model filiform Lie superalgebras." Journal of Algebra and Its Applications 17, no. 04 (2018): 1850074. http://dx.doi.org/10.1142/s0219498818500743.

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Suppose the ground field [Formula: see text] is an algebraically closed field of characteristic zero. By means of spectral sequences, the computation of the first cohomology group of the model filiform Lie superalgebra [Formula: see text] with coefficients in the adjoint module is reduced to the computation of the first cohomology group of an Abel ideal and a one-dimensional subalgebra. Then, by calculating the outer derivations, the algebra structure of the first cohomology group of [Formula: see text] is completely characterized.

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McCarthy, John D. "On the first cohomology group of cofinite subgroups in surface mapping class groups." Topology 40, no. 2 (2001): 401–18. http://dx.doi.org/10.1016/s0040-9383(99)00066-x.

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Dissertations / Theses on the topic "First Cohomology Group"

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Eastridge, Samuel Vance. "First l^2-Cohomology Groups." Thesis, Virginia Tech, 2015. http://hdl.handle.net/10919/52952.

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We want to take a look at the first cohomology group H^1(G, l^2(G)), in particular when G is locally-finite. First, though, we discuss some results about the space H^1(G, C G) for G locally-finite, as well as the space H^1(G, l^2(G)) when G is finitely generated. We show that, although in the case when G is finitely generated the embedding of C G into l^2(G) induces an embedding of the cohomology groups H^1(G, C G) into H^1(G, l^2(G)), when G is countably-infinite locally-finite, the induced homomorphism is not an embedding. However, even though the induced homomorphism is not an embedding,

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Eastridge, Samuel Vance. "First Cohomology of Some Infinitely Generated Groups." Diss., Virginia Tech, 2017. http://hdl.handle.net/10919/77517.

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The goal of this paper is to explore the first cohomology group of groups G that are not necessarily finitely generated. Our focus is on l^p-cohomology, 1 leq p leq infty, and what results regarding finitely generated groups change when G is infinitely generated. In particular, for abelian groups and locally finite groups, the l^p-cohomology is non-zero when G is countable, but vanishes when G has sufficient cardinality. We then show that the l^infty-cohomology remains unchanged for many classes of groups, before looking at several results regarding the injectivity of induced maps from embe

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Silva, Leda da [UNESP]. "Forma cohomológica do Teorema de Cauchy." Universidade Estadual Paulista (UNESP), 2010. http://hdl.handle.net/11449/91151.

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Made available in DSpace on 2014-06-11T19:24:55Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-05-04Bitstream added on 2014-06-13T18:06:54Z : No. of bitstreams: 1 silva_l_me_rcla.pdf: 767647 bytes, checksum: 77c93a6aec1e31ebbe544fac7c6cb314 (MD5)<br>O objetivo desta dissertação é apresentar uma abordagem cohomológica do Teorema de Cauchy e alguns resultados equivalentes a que um subconjunto aberto e conexo de C seja simplesmente conexo. Ressaltamos que um dos objetivos desta dissertação, inserida no Mestrado Profissional, Matemática Universitária, é estabelecer uma conexão entre as d

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Silva, Leda da. "Forma cohomológica do Teorema de Cauchy /." Rio Claro : [s.n.], 2010. http://hdl.handle.net/11449/91151.

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Orientador: Alice Kimie Miwa Libardi<br>Banca: João Peres Vieira<br>Banca: Gerson Petronilho<br>Resumo: O objetivo desta dissertação é apresentar uma abordagem cohomológica do Teorema de Cauchy e alguns resultados equivalentes a que um subconjunto aberto e conexo de C seja simplesmente conexo. Ressaltamos que um dos objetivos desta dissertação, inserida no Mestrado Profissional, Matemática Universitária, é estabelecer uma conexão entre as diversas áreas da Matemática, dando uma visão global da mesma, necessária ao professor universitário. Desta forma, o tema escolhido "Teorema de Cauchy"é um a

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Books on the topic "First Cohomology Group"

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Bárcenas, Noé, and Monica Moreno Rocha. Mexican mathematicians abroad: Recent contributions : first workshop, Matematicos Mexicanos Jovenes en el Mundo, August 22-24, 2012, Centro de Investigacion en Matematicas, A.C., Guanajuato, Mexico. Edited by Galaz-García Fernando editor. American Mathematical Society, 2016.

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Tu, Loring W. Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.001.0001.

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Equivariant cohomology is concerned with the algebraic topology of spaces with a group action, or in other words, with symmetries of spaces. First defined in the 1950s, it has been introduced into K-theory and algebraic geometry, but it is in algebraic topology that the concepts are the most transparent and the proofs are the simplest. One of the most useful applications of equivariant cohomology is the equivariant localization theorem of Atiyah–Bott and Berline–Vergne, which converts the integral of an equivariant differential form into a finite sum over the fixed point set of the group actio

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Murre, Jacob. Lectures on Algebraic Cycles and Chow Groups. Edited by Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161341.003.0009.

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This chapter showcases five lectures on algebraic cycles and Chow groups. The first two lectures are over an arbitrary field, where they examine algebraic cycles, Chow groups, and equivalence relations. The second lecture also offers a short survey on the results for divisors. The next two lectures are over the complex numbers. The first of these features discussions on the cycle map, the intermediate Jacobian, Abel–Jacobi map, and the Deligne cohomology. The following lecture focuses on algebraic versus homological equivalence, as well as the Griffiths group. The final lecture, which returns

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Cataldo, Mark Andrea de, Luca Migliorini Lectures 4–5, and Mark Andrea de Cataldo. The Hodge Theory of Maps. Edited by Eduardo Cattani, Fouad El Zein, Phillip A. Griffiths, and Lê Dũng Tráng. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691161341.003.0006.

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This chapter showcases two further lectures on the Hodge theory of maps, and they are mostly composed of exercises. The first lecture details a minimalist approach to sheaf cohomology, and then turns to the intersection cohomology complex, which is limited to the definition and calculation of the intersection complex Isubscript X of a variety of dimension d with one isolated singularity. Finally, this lecture discusses the Verdier duality. The second lecture sets out the Decomposition theorem, which is the deepest known fact concerning the homology of algebraic varieties. It then considers the

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Haesemeyer, Christian, and Charles A. Weibel. The Norm Residue Theorem in Motivic Cohomology. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691191041.001.0001.

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This book presents the complete proof of the Bloch–Kato conjecture and several related conjectures of Beilinson and Lichtenbaum in algebraic geometry. Brought together here for the first time, these conjectures describe the structure of étale cohomology and its relation to motivic cohomology and Chow groups. Although the proof relies on the work of several people, it is credited primarily to Vladimir Voevodsky. The book draws on a multitude of published and unpublished sources to explain the large-scale structure of Voevodsky's proof and introduces the key figures behind its development. It pr

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Voisin, Claire. Introduction. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691160504.003.0001.

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This chapter discusses some crucial notions to the interplay between cohomology and Chow groups, and also to the consequences, for the topology of a family of smooth projective varieties, of statements concerning Chow groups of the general or very general fiber. It surveys the main ideas and results presented throughout this volume. First, the chapter discusses the decomposition of the diagonal and spread. It then explains the generalized Bloch conjecture, the converse to the generalized decomposition of the diagonal. Next, the chapter turns to the decomposition of the small diagonal and its a

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Tretkoff, Paula. Topological Invariants and Differential Geometry. Princeton University Press, 2017. http://dx.doi.org/10.23943/princeton/9780691144771.003.0002.

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This chapter deals with topological invariants and differential geometry. It first considers a topological space X for which singular homology and cohomology are defined, along with the Euler number e(X). The Euler number, also known as the Euler-Poincaré characteristic, is an important invariant of a topological space X. It generalizes the notion of the cardinality of a finite set. The chapter presents the simple formulas for computing the Euler-Poincaré characteristic (Euler number) of many of the spaces to be encountered throughout the book. It also discusses fundamental groups and covering

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Book chapters on the topic "First Cohomology Group"

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Guralnick, Robert M. "The dimension of the first cohomology group." In Representation Theory II Groups and Orders. Springer Berlin Heidelberg, 1986. http://dx.doi.org/10.1007/bfb0075290.

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Guralnick, Robert M., and Cornelius Hoffman. "The First Cohomology Group and Generation of Simple Groups." In Groups and Geometries. Birkhäuser Basel, 1998. http://dx.doi.org/10.1007/978-3-0348-8819-6_7.

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Jantzen, Jens C. "First Cohomology Groups for Classical Lie Algebras." In Representation Theory of Finite Groups and Finite-Dimensional Algebras. Birkhäuser Basel, 1991. http://dx.doi.org/10.1007/978-3-0348-8658-1_11.

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Cegarra, A. M., A. R. Garzon, and P. Carrasco. "An exact sequence in the first variable for non-abelian cohomology in algebraic categories. A mayer-vietoris sequence for non-abelian cohomology of groups." In Lecture Notes in Mathematics. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/bfb0081349.

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Tu, Loring W. "A Universal Bundle for a Compact Lie Group." In Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0008.

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This chapter looks at a universal bundle for a compact Lie group. By Milnor's construction, every topological group has a universal bundle. Independently of Milnor's result, the chapter constructs a universal bundle for any compact Lie group G. This construction is based on the fact that every compact Lie group can be embedded as a subgroup of some orthogonal group O(k). The chapter first constructs a universal O(k)-bundle by finding a weakly contractible space on which O(k) acts freely. The infinite Stiefel variety V (k, ∞) is such a space. As a subgroup of O(k), the compact Lie group G will also act freely on V (k, ∞), thereby producing a universal G-bundle.

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Tu, Loring W. "Fundamental Vector Fields." In Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0011.

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This chapter addresses fundamental vector fields. The concept of a connection on a principal bundle is essential in the construction of the Cartan model. To define a connection on a principal bundle, one first needs to define the fundamental vector fields. When a Lie group acts smoothly on a manifold, every element of the Lie algebra of the Lie group generates a vector field on the manifold called a fundamental vector field. On a principal bundle, the fundamental vectors are precisely the vertical tangent vectors. In general, there is a relation between zeros of fundamental vector fields and fixed points of the group action. Unless specified otherwise (such as on a principal bundle), a group action is assumed to be a left action.

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Tu, Loring W. "Differential Graded Algebras." In Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0018.

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This chapter investigates differential graded algebras. Throughout the chapter, G will be a Lie group with Lie algebra g. On a manifold M, the de Rham complex is a differential graded algebra, a graded algebra that is also a differential complex. If the Lie group G acts smoothly on M, then the de Rham complex Ω‎(M) is more than a differential graded algebra. It has in addition two actions of the Lie algebra: interior multiplication and the Lie derivative. A differential graded algebra Ω‎ with an interior multiplication and a Lie derivative satisfying Cartan's homotopy formula is called a g-differential graded algebra. To construct an algebraic model for equivariant cohomology, the chapter first constructs an algebraic model for the total space EG of the universal G-bundle. It is a g-differential graded algebra called the Weil algebra.

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Tu, Loring W. "Curvature on a Principal Bundle." In Introductory Lectures on Equivariant Cohomology. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691191751.003.0017.

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This chapter examines curvature on a principal bundle. The curvature of a connection on a principal G-bundle is a g-valued 2-form that measures, in some sense, the deviation of the connection from the Maurer-Cartan connection on a product bundle. The Maurer-Cartan form Θ‎ on a Lie group G satisfies the Maurer-Cartan equation. Let M be a smooth manifold. The chapter then pulls the Maurer-Cartan equation back and uses Proposition 14.3 to get the Maurer-Cartan connection. It also considers the second structural equation; the first structural equation is discussed in a previous chapter. Finally, the chapter derives some properties of the curvature form.

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Tanasa, Adrian. "Quantum gravity, group field theory (GFT), and combinatorics." In Combinatorial Physics. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192895493.003.0010.

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This chapter is the first chapter of the book dedicated to the study of the combinatorics of various quantum gravity approaches. After a brief introductory section to quantum gravity, we shortly mention the main candidates for a quantum theory of gravity: string theory, loop quantum gravity, and group field theory (GFT), causal dynamical triangulations, matrix models. The next sections introduce some GFT models such as the Boulatov model, the colourable and the multi-orientable model. The saddle point method for some specific GFT Feynman integrals is presented in the fifth section. Finally, some algebraic combinatorics results are presented: definition of an appropriate Conne–Kreimer Hopf algebra describing the combinatorics of the renormalization of a certain tensor GFT model (the so-called Ben Geloun–Rivasseau model) and the use of its Hochschild cohomology for the study of the combinatorial Dyson–Schwinger equation of this specific model.

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Haesemeyer, Christian, and Charles A. Weibel. "Rost’s Chain Lemma." In The Norm Residue Theorem in Motivic Cohomology. Princeton University Press, 2019. http://dx.doi.org/10.23943/princeton/9780691191041.003.0009.

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This chapter states and proves Rost's Chain Lemma. The proof (due to Markus Rost) does not use the inductive assumption that BL(n − 1) holds. Throughout this chapter, 𝓁 is a fixed prime, and 𝑘 is a field containing 1/𝓁 and all 𝓁<sup>th</sup> roots of unity. It fixes an integer 𝑛 ≥ 2 and an 𝑛-tuple (𝑎<sub>1</sub>, ..., 𝑎<sub>𝑛</sub>) of units in 𝑘, such that the symbol ª = {𝑎<sub>1</sub>, ..., 𝑎<sub>𝑛</sub>} is nontrivial in the Milnor 𝐾-group 𝐾<sup>𝑀</sup> <sub>𝑛</sub>(𝑘)/𝓁. The chapter produces the statement of the Chain Lemma by first proving the special case 𝑛 = 2. The notion of an 𝓁-form on a locally free sheaf over 𝑆 is then introduced, before the chapter shows how 𝓁-forms may be used to define elements of 𝐾<sup>𝑀</sup> <sub>𝑛</sub>(𝑘(𝑆))/𝓁.

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