Pattern-equivariant cohomology of tiling spaces with rotations

dc.contributor.advisorSadun, Lorenzoen
dc.creatorRand, Betseygailen
dc.date.accessioned2008-08-28T23:09:24Zen
dc.date.available2008-08-28T23:09:24Zen
dc.date.issued2006en
dc.descriptiontexten
dc.description.abstractThis paper develops a new cohomology theory on generalized tiling spaces. This theory incorporates both the rotational geometry of the tiling space and the local pattern geometry into the structure of the cohomology groups. Our use of the local pattern geometry is a generalization of pattern-equivariant cohomology, a theory developed by Ian Putnam and Johannes Kellendonk in 2003. It was defined for tilings whose tiles appear as translates. The most general setting in tiling theory is to work with tiling spaces, with an action of a subgroup of the Euclidean group. This paper defines a new, general pattern-equivariant cohomology for tiling spaces with finite rotation groups, and proves that it is preserved under homeomorphisms which commute with the action of the group. It is conjectured here that this theory is not a topological invariant for tiling spaces with infinite rotation group.
dc.description.departmentMathematicsen
dc.format.mediumelectronicen
dc.identifierb65489640en
dc.identifier.oclc156945091en
dc.identifier.urihttp://hdl.handle.net/2152/2798en
dc.language.isoengen
dc.rightsCopyright is held by the author. Presentation of this material on the Libraries' web site by University Libraries, The University of Texas at Austin was made possible under a limited license grant from the author who has retained all copyrights in the works.en
dc.subject.lcshTiling (Mathematics)en
dc.subject.lcshHomology theoryen
dc.subject.lcshRotation groupsen
dc.titlePattern-equivariant cohomology of tiling spaces with rotationsen
dc.type.genreThesisen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen

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