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dc.contributor.advisorAllcock, Daniel, 1969-en
dc.creatorMark, Alice Harwayen
dc.date.accessioned2015-10-02T18:15:36Zen
dc.date.available2015-10-02T18:15:36Zen
dc.date.issued2015-05en
dc.date.submittedMay 2015en
dc.identifierdoi:10.15781/T2N300en
dc.identifier.urihttp://hdl.handle.net/2152/31507en
dc.descriptiontexten
dc.description.abstractThere are 432 strongly squarefree symmetric bilinear forms of signature (2,1) defined over Z([square root of 2]) whose integral isometry groups are generated up to finite index by finitely many reflections. We adapted Allcock's method (based on Nikulin's) of analysis for the 2-dimensional Weyl chamber to the real quadratic setting, and used it to produce a finite list of quadratic forms which contains all of the ones of interest to us as a sub-list. The standard method for determining whether a hyperbolic reflection group is generated up to finite index by reflections is an algorithm of Vinberg. However, for a large number of our quadratic forms the computation time required by Vinberg's algorithm was too long. We invented some alternatives, which we present here.en
dc.format.mimetypeapplication/pdfen
dc.language.isoenen
dc.subjectHyperbolic reflection groupsen
dc.titleThe classification of rank 3 reflective hyperbolic lattices over Z([square root of 2])en
dc.typeThesisen
dc.date.updated2015-10-02T18:15:37Zen
dc.contributor.committeeMemberReid, Alanen
dc.contributor.committeeMemberBowen, Lewisen
dc.contributor.committeeMemberGordon, Cameronen
dc.contributor.committeeMemberAgol, Ianen
dc.description.departmentMathematicsen
thesis.degree.departmentMathematicsen
thesis.degree.disciplineMathematicsen
thesis.degree.grantorThe University of Texas at Austinen
thesis.degree.levelDoctoralen
thesis.degree.nameDoctor of Philosophyen
dc.creator.orcid0000-0001-8823-7456en


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