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Cubulating one-relator groups with torsion

Published online by Cambridge University Press:  25 July 2013

JOSEPH LAUER  and
DANIEL T. WISE
JOSEPH LAUER
Affiliation:
Dept. of Mathematics & Statistics, McGill University, Montreal, QC, Canada. e-mail: lauer@math.mit.edu, wise@math.mcgill.ca
DANIEL T. WISE
Affiliation:
Dept. of Mathematics & Statistics, McGill University, Montreal, QC, Canada. e-mail: lauer@math.mit.edu, wise@math.mcgill.ca
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Abstract

Let 〈a1, . . ., am ∣ wn〉 be a presentation of a group G, where n ≥ 2. We define a system of codimension-1 subspaces in the universal cover, and invoke Sageev's construction to produce an action of G on a CAT(0) cube complex. We show that the action is proper and cocompact when n ≥ 4. A fundamental tool is a geometric generalization of Pride's C(2n) small-cancellation result. We prove similar results for staggered groups with torsion.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 3 , November 2013 , pp. 411 - 429
Copyright
Copyright © Cambridge Philosophical Society 2013 

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