Towards computing the rational homology and assembly maps of generalised Thompson groups

Abstract

Let $V_r(\Sigma )$ be the generalised Thompson group defined as the automorphism group of a valid, bounded, and complete Cantor algebra. We show that that for every $n>0$ there is a $k>n,$ such that there exists a $k$-dimensional $n$-connected simplicial complex $K$ such that $V_r(\Sigma )$ acts on $K$ with finite stabilisers. We also determine the number of conjugacy classes of finite cyclic subgroups of a given order $m$ in Brin-Thompson groups. We apply our computations to the rationalised Farrell-Jones assembly map in algebraic $K$-theory.

12 pages There was a mistake in a previous version of this preprint. We no longer compute the rational homology of generalized Brin-Higman-Thompson groups

References in corpus (1)

• Algebraic K-theory of group rings and the cyclotomic trace map