The large scale geometry of strongly aperiodic subshifts of finite type

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dc.contributor.advisorPutman, Thomas Andrew
dc.contributor.committeeMemberCox, Steven J
dc.contributor.committeeMemberVeech, William A
dc.creatorCohen, David Bruce
dc.date.accessioned2016-01-07T17:18:55Z
dc.date.available2016-01-07T17:18:55Z
dc.date.created2015-05
dc.date.issued2015-04-22
dc.date.submittedMay 2015
dc.date.updated2016-01-07T17:18:55Z
dc.description.abstractA 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.
dc.format.mimetypeapplication/pdf
dc.identifier.citationCohen, 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>.
dc.identifier.urihttps://hdl.handle.net/1911/87754
dc.language.isoeng
dc.rightsCopyright 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.
dc.subjectgeometric group theory
dc.subjectsymbolic dynamics
dc.titleThe large scale geometry of strongly aperiodic subshifts of finite type
dc.typeThesis
dc.type.materialText
thesis.degree.departmentMathematics
thesis.degree.disciplineNatural Sciences
thesis.degree.grantorRice University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy
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