Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

The geometry of one-relator groups satisfying a polynomial isoperimetric inequality


Authors: Giles Gardam and Daniel J. Woodhouse
Journal: Proc. Amer. Math. Soc. 147 (2019), 125-129
MSC (2010): Primary 20F65; Secondary 20F67, 20E06, 20F05
DOI: https://doi.org/10.1090/proc/14238
Published electronically: October 18, 2018
MathSciNet review: 3876736
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: For every pair of positive integers $ p > q$ we construct a one-relator group $ R_{p,q}$ whose Dehn function is $ \simeq n^{2 \alpha }$ where $ \alpha = \log _2(2p / q)$. The group $ R_{p, q}$ has no subgroup isomorphic to a Baumslag-Solitar group $ BS(m, n)$ with $ m \neq \pm n$, but it is not automatic, not CAT(0), and cannot act freely on a CAT(0) cube complex. This answers a long-standing question on the automaticity of one-relator groups and gives counterexamples to a conjecture of Wise.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 20F65, 20F67, 20E06, 20F05

Retrieve articles in all journals with MSC (2010): 20F65, 20F67, 20E06, 20F05


Additional Information

Giles Gardam
Affiliation: Department of Mathematics, Technion, Haifa, Israel
Email: gilesgar@technion.ac.il

Daniel J. Woodhouse
Affiliation: Department of Mathematics, Technion, Haifa, Israel
Email: woodhouse.da@technion.ac.il

DOI: https://doi.org/10.1090/proc/14238
Keywords: One-relator groups, Dehn functions, automatic groups, CAT(0) spaces, CAT(0) cube complexes, Baumslag--Solitar subgroups
Received by editor(s): December 8, 2017
Received by editor(s) in revised form: May 3, 2018
Published electronically: October 18, 2018
Additional Notes: The first author was supported by the Israel Science Foundation (grant 662/15).
The second author was supported by the Israel Science Foundation (grant 1026/15).
Communicated by: David Futer
Article copyright: © Copyright 2018 American Mathematical Society