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dc.contributor.advisorChairperson, Graduate Committee: Marcy Barge.en
dc.contributor.authorOlimb, Carl Andrew.en
dc.date.accessioned2013-06-25T18:43:07Z
dc.date.available2013-06-25T18:43:07Z
dc.date.issued2010en
dc.identifier.urihttps://scholarworks.montana.edu/xmlui/handle/1/1985
dc.description.abstractWe explore the asymptotic arc components made by the continuous R²-action of translation on two-dimensional nonperiodic substitution tiling spaces. As there is a strong connection between the topology of a tiling space and the tiling dynamics that it supports, the results in this dissertation represent a qualitative approach to the study of tiling dynamics. Our results are the establishment of techniques to isolate and visualize the asymptotic behavior. In a recent paper, Barge, et al, showed the cohomology formed from the asymptotic structure in one-dimensional Pisot substitution tiling spaces is a topological invariant, [BDS]. However, in one dimension there exist only a finite number of asymptotic pairs, whereas there are infinitely many asymptotic leaves in two dimensions. By considering periodic tilings that are asymptotic in more than a half plane we are able to use the stable manifold under inflation and substitution to show there are a finite number of 'directions' of branching. This yields a description of the asymptotic structure in terms of an inverse limit of a branched set in the approximating collared Anderson-Putnam complex. Using rigidity results from [JK], we show the cohomology formed from the asymptotic structure is a topological invariant.en
dc.language.isoengen
dc.publisherMontana State University - Bozeman, College of Letters & Scienceen
dc.subject.lcshCohomology operations.en
dc.subject.lcshTiling spaces.en
dc.subject.lcshTorsion.en
dc.titleThe branch locus for two dimensional tiling spaces
dc.typeDissertation
dc.rights.holderCopyright Carl Andrew Olimb 2010en
thesis.catalog.ckey1534691en
thesis.degree.committeemembersMembers, Graduate Committee: Richard Swanson (co-chair); Lukas Geyer; Russell Walker; Jack D. Dockeryen
thesis.degree.departmentMathematical Sciences.en
thesis.degree.genreDissertationen
thesis.degree.namePhDen
thesis.format.extentfirstpage1en
thesis.format.extentlastpage83en
mus.identifier.categoryPhysics & Mathematics
mus.relation.departmentMathematical Sciences.en_US
mus.relation.universityMontana State University - Bozemanen_US


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