Torsion cohomology for solvable groups of finite rank

2014/06/14 by Karl Lorensen, Lorensen, Karl
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology #Algebraic structures and combinatorial models

paper · pdf · doi:10.48550/arxiv.1406.3731

Abstract

We define a class U of solvable groups of finite abelian section rank which includes all such groups that are virtually torsion-free as well as those that are finitely generated. Assume that G is a group in U and A a \mathbb ZG-module. If A is \mathbb Z-torsion-free and has finite \mathbb Z-rank, we stipulate a condition on A that guarantees that Hⁿ(G,A) and H_n(G,A) must be finite for n≥ 0. Moreover, if the underlying abelian group of A is a Černikov group, we identify a similar condition on A that ensures that Hⁿ(G,A) must be a Černikov group for all n≥ 0.

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