arXiv Analytics

Sign in

arXiv:1412.4572 [math.GR]AbstractReferencesReviewsResources

The large scale geometry of strongly aperiodic subshifts of finite type

David Bruce Cohen

Published 2014-12-15Version 1

A subshift on a group G is a closed, G-invariant subset of A^G, for some finite set A. It is said to be of finite type if it is defined by a finite collection of "forbidden patterns" and to be strongly aperiodic if it has no points fixed by a nontrivial element of the group. We show that if G has at least two ends, then there are no strongly aperiodic subshifts of finite type on G (as was previously known for free groups). Additionally, we show that among torsion free, finitely presented groups, the property of having a strongly aperiodic subshift of finite type is invariant under quasi isometry.

Comments: 28 pages, 6 figures
Categories: math.GR
Subjects: 20F65, 37B10
Related articles: Most relevant | Search more
arXiv:1706.01387 [math.GR] (Published 2017-06-05)
Strongly aperiodic subshifts of finite type on hyperbolic groups
arXiv:0807.4704 [math.GR] (Published 2008-07-29, updated 2008-10-27)
Large scale geometry of commutator subgroups
arXiv:1409.0125 [math.GR] (Published 2014-08-30)
On finite generation of self-similar groups of finite type