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