Vol. 266, No. 2, 2013

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The Brin–Thompson groups sV are of type F

Martin G. Fluch, Marco Marschler, Stefan Witzel and Matthew C. B. Zaremsky

Vol. 266 (2013), No. 2, 283–295
Abstract

We prove that the Brin–Thompson groups sV , also called higher-dimensional Thompson’s groups, are of type F for all s . This result was previously shown for s 3, by considering the action of sV on a naturally associated space. Our key step is to replace this space by a subspace sX that is easier to analyze.

Keywords
Thompson’s groups, finiteness properties
Mathematical Subject Classification 2010
Primary: 20F65
Secondary: 57Q12
Milestones
Received: 12 September 2012
Revised: 20 November 2012
Accepted: 25 November 2012
Published: 12 November 2013
Authors
Martin G. Fluch
Department of Mathematics
Bielefeld University
PO Box 100131
D-33501 Bielefeld
Germany
Marco Marschler
Department of Mathematics
Bielefeld University
PO Box 100131
D-33501 Bielefeld
Germany
Stefan Witzel
Mathematical Institute
University of Münster
Einsteinstraße 62
D-48149 Münster
Germany
Matthew C. B. Zaremsky
Department of Mathematical Sciences
Binghamton University
Binghamton, NY 13902
United States