Putman, Thomas Andrew2016-01-072016-01-072015-052015-04-22May 2015Cohen, David Bruce. "The large scale geometry of strongly aperiodic subshifts of finite type." (2015) Diss., Rice University. <a href="https://hdl.handle.net/1911/87754">https://hdl.handle.net/1911/87754</a>.https://hdl.handle.net/1911/87754A 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.application/pdfengCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.geometric group theorysymbolic dynamicsThesis2016-01-07