Arithmetic reflection groups and congruence subgroups

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dc.contributor.advisorReid, Alan W.en
dc.contributor.committeeMemberAllcock, Danielen
dc.contributor.committeeMemberGordon, Cameronen
dc.contributor.committeeMemberLuecke, Johnen
dc.contributor.committeeMemberNamazi, Hosseinen
dc.contributor.committeeMemberRamachandran, Vijayaen
dc.creatorLakeland, Grant Stephenen
dc.date.accessioned2012-07-12T21:21:52Zen
dc.date.accessioned2017-05-11T22:25:50Z
dc.date.available2012-07-12T21:21:52Zen
dc.date.available2017-05-11T22:25:50Z
dc.date.issued2012-05en
dc.date.submittedMay 2012en
dc.date.updated2012-07-12T21:21:58Zen
dc.descriptiontexten
dc.description.abstractThis thesis investigates the geometric and topological constraints placed on the quotient space of a Fuchsian or Kleinian group by requiring that the group admits a fundamental domain which is simultaneously a Ford domain and a Dirichlet domain. In the case of Fuchsian groups, a direct correspondence with reflection groups is proved, and this result is used to first find explicitly the 23 non-cocompact arithmetic maximal hyperbolic reflection groups in the group of isometries of the hyperbolic plane, and subsequently to test whether these groups are all congruence. In the case of Kleinian groups, similar results are shown, and some examples of reflection groups are considered.en
dc.description.departmentMathematicsen
dc.format.mimetypeapplication/pdfen
dc.identifier.slug2152/ETD-UT-2012-05-5179en
dc.identifier.urihttp://hdl.handle.net/2152/ETD-UT-2012-05-5179en
dc.language.isoengen
dc.subjectArithmetic reflection groupen
dc.subjectCongruenceen
dc.subjectFundamental domainen
dc.titleArithmetic reflection groups and congruence subgroupsen
dc.type.genrethesisen

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