Subexponential group cohomology and the K-theory of Lafforgue's algebra A_{max}(pi)

TL;DR

This paper demonstrates that for finitely generated groups, certain cohomology classes with subexponential growth can be extended over the topological K-theory of Lafforgue's algebra, linking group cohomology with algebraic K-theory.

Contribution

It establishes a connection between subexponential group cohomology classes and their extendability over Lafforgue's algebra K-theory, a novel insight in the field.

Findings

Cohomology classes with subexponential growth are extendable over Lafforgue's algebra.

Provides a new method to relate group cohomology to algebraic K-theory.

Enhances understanding of the structure of Lafforgue's algebra in relation to group properties.

Abstract

We show that for any finitely generated group G, group cohomology classes represented by cocycles of subexponential growth are extendable over the topological K-groups of the Lafforgue algebra associated to G.