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Tubular Free by Cyclic Groups Act Freely on CAT(0) Cube Complexes

Published online by Cambridge University Press:  20 November 2018

Jack Button
Jack Button*
Affiliation:
Selwyn College, University of Cambridge, Cambridge CB3 9DQ, UK e-mail: j.o.button@dpmms.cam.ac.uk
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Abstract

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We identify when a tubular group (the fundamental group of a finite graph of groups with ${{\mathbb{Z}}^{2}}$ vertex and $\mathbb{Z}$ edge groups) is free by cyclic and show, using Wise’s equitable sets criterion, that every tubular free by cyclic group acts freely on a $\text{CAT}\left( 0 \right)$ cube complex.

Keywords

20F6520F6720E08CAT(0)tubular group
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 1 , 01 March 2017 , pp. 54 - 62
Copyright
Copyright © Canadian Mathematical Society 2017

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