Homomorphisms of the Fundamental Group of a Surface into PSU(1,1), and the Action of the Mapping Class Group.

Persistent Link:
http://hdl.handle.net/10150/193713
Title:
Homomorphisms of the Fundamental Group of a Surface into PSU(1,1), and the Action of the Mapping Class Group.
Author:
Konstantinou, Panagiota
Issue Date:
2006
Publisher:
The University of Arizona.
Rights:
Copyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.
Abstract:
In this paper we consider the action of the mapping class group of a surface on the space of homomorphisms from the fundamental group of a surface into PSU(1,1). Goldman conjectured that when the surface is closed and of genus bigger than one, the action on non-Teichmuller connected components of the associated moduli space (i.e. the space of homomorphisms modulo conjugation) is ergodic. One approach to this question is to use sewing techniques which requires that one considers the action on the level of homomorphisms, and for surfaces with boundary. In this paper we consider the case of the one-holed torus with boundary condition, and we determine regions where the action is ergodic. This uses a combination of techniques developed by Goldman, and Pickrell and Xia. The basic result is an analogue of the result of Goldman's at the level of moduli.
Type:
text; Electronic Dissertation
Keywords:
representation varieties; mapping class group; teichmuller space; ergodic action
Degree Name:
PhD
Degree Level:
doctoral
Degree Program:
Mathematics; Graduate College
Degree Grantor:
University of Arizona
Advisor:
Pickrell, Douglas
Committee Chair:
Pickrell, Douglas

Full metadata record

DC FieldValue Language
dc.language.isoENen_US
dc.titleHomomorphisms of the Fundamental Group of a Surface into PSU(1,1), and the Action of the Mapping Class Group.en_US
dc.creatorKonstantinou, Panagiotaen_US
dc.contributor.authorKonstantinou, Panagiotaen_US
dc.date.issued2006en_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.description.abstractIn this paper we consider the action of the mapping class group of a surface on the space of homomorphisms from the fundamental group of a surface into PSU(1,1). Goldman conjectured that when the surface is closed and of genus bigger than one, the action on non-Teichmuller connected components of the associated moduli space (i.e. the space of homomorphisms modulo conjugation) is ergodic. One approach to this question is to use sewing techniques which requires that one considers the action on the level of homomorphisms, and for surfaces with boundary. In this paper we consider the case of the one-holed torus with boundary condition, and we determine regions where the action is ergodic. This uses a combination of techniques developed by Goldman, and Pickrell and Xia. The basic result is an analogue of the result of Goldman's at the level of moduli.en_US
dc.typetexten_US
dc.typeElectronic Dissertationen_US
dc.subjectrepresentation varietiesen_US
dc.subjectmapping class groupen_US
dc.subjectteichmuller spaceen_US
dc.subjectergodic actionen_US
thesis.degree.namePhDen_US
thesis.degree.leveldoctoralen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.grantorUniversity of Arizonaen_US
dc.contributor.advisorPickrell, Douglasen_US
dc.contributor.chairPickrell, Douglasen_US
dc.contributor.committeememberPickrell, Douglasen_US
dc.contributor.committeememberFoth, Phillipen_US
dc.contributor.committeememberGlickenstein, Daviden_US
dc.contributor.committeememberUlmer, Douglasen_US
dc.identifier.proquest1653en_US
dc.identifier.oclc137356637en_US
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