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

  Published:2016-12-09
 Printed: Mar 2017
  • Jack Button,
    Selwyn College, University of Cambridge, Cambridge CB3 9DQ, UK
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Abstract

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 CAT(0) cube complex.
Keywords: CAT(0), tubular group CAT(0), tubular group
MSC Classifications: 20F65, 20F67, 20E08 show english descriptions Geometric group theory [See also 05C25, 20E08, 57Mxx]
Hyperbolic groups and nonpositively curved groups
Groups acting on trees [See also 20F65]
20F65 - Geometric group theory [See also 05C25, 20E08, 57Mxx]
20F67 - Hyperbolic groups and nonpositively curved groups
20E08 - Groups acting on trees [See also 20F65]
 

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