Volume 16, issue 4 (2016)

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Stability results for Houghton groups

Peter Patzt and Xiaolei Wu

Algebraic & Geometric Topology 16 (2016) 2365–2377
Abstract

We prove homological stability for a twisted version of the Houghton groups and their multidimensional analogues. Based on this, we can describe the homology of the Houghton groups and that of their multidimensional analogues over constant noetherian coefficients as an essentially finitely generated $\mathsf{FI}$–module.

Keywords
homology stability, representation stability, Houghton groups
Mathematical Subject Classification 2010
Primary: 18D10, 20J06, 55U05
Publication
Published: 12 September 2016
Authors
 Peter Patzt Institut für Mathematik Freie Universität 14195 Berlin Germany Xiaolei Wu Max Planck Institute for Mathematics 53111 Bonn Germany