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arXiv · 1605.00840

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

Conchita Martínez-Pérez·Brita Nucinkis
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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.

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Conchita Martínez-Pérez, Brita Nucinkis. 2016-05-03. Towards computing the rational homology and assembly maps of generalised Thompson groups. https://arxiv.org/abs/1605.00840

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