The large scale geometry of strongly aperiodic subshifts of finite type

Date
2015-04-22
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Abstract

A subshift on a group G is a closed, G-invariant subset of A to the 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.

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Degree
Doctor of Philosophy
Type
Thesis
Keywords
geometric group theory, symbolic dynamics
Citation

Cohen, David Bruce. "The large scale geometry of strongly aperiodic subshifts of finite type." (2015) Diss., Rice University. https://hdl.handle.net/1911/87754.

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