Cohomology of Γ-groups

Each Γ−monoidal extension of a Gr−category is determined by a factor set on a group Γ. In the paper "The Factor Sets of Gr-Categories of the Type (Π, A)", we shall show that the such factor set can be reduced and induces a 3-cocycle of Γ−groups.

14p runordie5 04-07-2022 8 2   Download

In the first chapter, we introduce the concept of profinite groups and study their basic properties; We define cohomology groups and investigate their functorial properties; Then we introduce Galois descent and give a correspondence between equivalence classes of twisted forms and cohomology classes under some conditions which will be described explicitly.

125p viabigailjohnson 10-06-2022 10 2   Download

In this paper, we present the concept of strict factor set on the group Γ with coefficients in categorical groups of the type (Π, A). We define the element h ∈ H3 Γ and give a new interpretation of cohomology groups with third-dimensional operator Γ. The element h determines a 1-1 correspondence between classes of factor sets on Γ with coefficients in (Π, A) and group H3 Γ (Π, A).

9p tradaviahe12 06-01-2021 15 1   Download

This paper is meant to give a brief survey on Quillen conjecture and finally present a recent result that this conjecture has been verified by the authors.

4p viminotaur2711 29-10-2019 21 1   Download

In this paper we compute the integral homology of the Borel subgroup B of the special linear group SL(2,Fp) where p is a prime. In order to compute the integral homology of B, we decompose it into ℓ− primary parts.

6p viminotaur2711 29-10-2019 14 0   Download

In this paper, we study the relationships between the cohomological structure of a space and that of the fixed point set of a finite dimensional pro-torus action on the space. This paper is about finite dimensional compact groups. The concept of the dimension of a compact topological group plays an essential role in transformation group theory.

9p nutifooddau 21-01-2019 30 1   Download

Using the Guichardet construction, we compute the cohomology groups of a complex of free Lie algebras introduced by Alekseev and Torossian.

7p tuongvidanh 06-01-2019 27 1   Download

In the study of the theory of irreducible unitary representations, is necessary to analyze and demonstrate diverse results on integral orbital of functions belonging to the cohomology Hi (g, K; V  V*), and that it is wanted they belong to the L2(G)-cohomology of their reducible unitary representations called discrete series. Then is necessary consider the Frèchet space I(G), and analyze the 2-integrability to the fibers of the space G/K, in spaces or locally compact components of G/K.

194p lyly_5 22-03-2013 46 3   Download

We prove the strong Macdonald conjecture of Hanlon and Feigin for reductive groups G. In a geometric reformulation, we show that the Dolbeault cohomology H q (X; Ωp ) of the loop Grassmannian X is freely generated by de Rham’s forms on the disk coupled to the indecomposables of H • (BG). Equating the two Euler characteristics gives an identity, independently known to Macdonald [M], which generalises Ramanujan’s 1 ψ1 sum. For simply laced root systems at level 1, we also find a ‘strong form’ of Bailey’s 4 ψ4 sum. ...

47p dontetvui 17-01-2013 59 7   Download

In a classic paper, Gerstenhaber showed that first order deformations of an associative k-algebra a are controlled by the second Hochschild cohomology group of a. More generally, any n-parameter first order deformation of a gives, due to commutativity of the cup-product on Hochschild cohomology, a graded algebra morphism Sym• (kn ) → Ext2•bimod (a, a). We prove that any extension aof the n-parameter first order deformation of a to an infinite order formal deformation provides a canonical ‘lift’ of the graded algebra morphism above to a dg-algebra morphism Sym• (kn ) → RHom• ...

17p noel_noel 17-01-2013 52 4   Download

D. Mumford conjectured in [33] that the rational cohomology of the stable moduli space of Riemann surfaces is a polynomial algebra generated by certain classes κi of dimension 2i. For the purpose of calculating rational cohomology, one may replace the stable moduli space of Riemann surfaces by BΓ∞ , where Γ∞ is the group of isotopy classes of automorphisms of a smooth oriented connected surface of “large” genus. Tillmann’s theorem [44] that the plus construction makes BΓ∞ into an infinite loop space led to a stable homotopy version of Mumford’s conjecture, stronger than the original [24]. .

100p noel_noel 17-01-2013 37 6   Download

We establish new results and introduce new methods in the theory of measurable orbit equivalence, using bounded cohomology of group representations. Our rigidity statements hold for a wide (uncountable) class of groups arising from negative curvature geometry.

55p noel_noel 17-01-2013 60 7   Download

A Pierre Deligne, a l ’occasion de son 60-i`me anniversaire, ` e en t´moignage de profonde admiration e Abstract If V is a smooth projective variety defined over a local field K with fi¯ nite residue field, so that its ´tale cohomology over the algebraic closure K is e supported in codimension 1, then the mod p reduction of a projective regular model carries a rational point. As a consequence, if the Chow group of 0-cycles of V over a large algebraically closed field is trivial, then the mod p reduction of a projective regular model carries a rational...

17p noel_noel 17-01-2013 38 4   Download

I prove a formula expressing the descendent genus g Gromov-Witten invariants of a projective variety X in terms of genus 0 invariants of its symmetric product stack S g+1 (X). When X is a point, the latter are structure constants of the symmetric group, and we obtain a new way of calculating the GromovWitten invariants of a point. 1. Introduction Let X be a smooth projective variety. The genus 0 Gromov-Witten invariants of X satisfy relations which imply that they can be completely encoded in the structure of a Frobenius manifold on the cohomology H ∗ (X, C). ...

42p noel_noel 17-01-2013 40 7   Download

Dedicated to the memory of Barry Johnson, 1937–2002 Abstract The main result of this paper is that the k th continuous Hochschild cohomology groups H k (M, M) and H k (M, B(H)) of a von Neumann factor M ⊆ B(H) of type II1 with property Γ are zero for all positive integers k. The method of proof involves the construction of hyperfinite subfactors with special properties and a new inequality of Grothendieck type for multilinear maps. We prove joint continuity in the · 2 -norm of separately ultraweakly continuous multilinear maps, and combine these results to reduce to...

26p tuanloccuoi 04-01-2013 43 6   Download

Topological Hochschild homology and localization 2. The homotopy groups of T (A|K) 3. The de Rham-Witt complex and TR· (A|K; p) ∗ 4. Tate cohomology and the Tate spectrum 5. The Tate spectral sequence for T (A|K) 6. The pro-system TR· (A|K; p, Z/pv ) ∗ Appendix A. Truncated polynomial algebras References Introduction In this paper we establish a connection between the Quillen K-theory of certain local fields and the de Rham-Witt complex of their rings of integers with logarithmic poles at the maximal ideal.

114p tuanloccuoi 04-01-2013 56 6   Download

Five years after the meeting "Quaternionic Structures in Mathematics and Physics", which took place at the International School for Advanced Studies (SISSA), Trieste, 5-9 September 1994, we felt it was time to have another meeting on the same subject to bring together scientists from both areas. The second Meeting on Quaternionic Structures in Mathematics and Physics was held in Rome, 6-10 September 1999.

486p camchuong_1 10-12-2012 70 7   Download

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Journal of Operator Theory đề tài: Cyclic cohomology của đại số nhóm của các nhóm tự do...

13p matuot_266 27-08-2011 48 6   Download