Group Cohomology and Lp-Cohomology of Finitely Generated Groups

2000]Primary: 43A15; Secondary: 20F65, 20F18 GROUP COHOMOLOGY AND L-COHOMOLOGY OF FINITELY GENERATED GROUPS

In this paper G will always be a finitely generated, infinite group and S will always be a symmetric generating set for G. Let M be a right G-module. A 1cocycle with values in M is a map δ : G → M such that δ(gh) = (δ(h)) g + δ(g) for any g, h ∈ G; a 1-coboundary is a 1-cocycle of the form δ(g) = xg − x for some x ∈ M and for all g ∈ G. We denote by Z (G,M) the vector space of all 1-cocycles an...

Locally-finitely-valued Cohomology Groups

Weakly Confluent Mappings and Finitely-generated Cohomology

In this paper we answer a question of Wayne Lewis by proving that if X is a one-dimensional, hereditarily indecomposable continuum and if HX(X) is finitely generated, then C(X), the hyperspace of subcontinua of X, has dimension 2. Let C(A) be the hyperspace of subcontinua of the continuum X with the topology determined by the Hausdorff metric. A classical theorem of J. L. Kelley [4] asserts tha...

A reductive group with finitely generated cohomology algebras

Let G be the linear algebraic group SL3 over a field k of characteristic two. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. We show that the full cohomology ring H∗(G, A) is finitely generated. This extends the finite generation property of the ring of invariants AG. We discuss where the problem stands for other geometrically reductiv...

4 A reductive group with finitely generated cohomology algebras .

Let G be the linear algebraic group SL3 over a field k of characteristic two. Let A be a finitely generated commutative k-algebra on which G acts rationally by k-algebra automorphisms. We show that the full cohomology ring H(G,A) is finitely generated. This extends the finite generation property of the ring of invariants AG. We discuss where the problem stands for other geometrically reductive ...