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.
| Identifer | oai:union.ndltd.org:arizona.edu/oai:arizona.openrepository.com:10150/193713 |
| Date | January 2006 |
| Creators | Konstantinou, Panagiota |
| Contributors | Pickrell, Douglas, Pickrell, Douglas, Pickrell, Douglas, Foth, Phillip, Glickenstein, David, Ulmer, Douglas |
| Publisher | The University of Arizona. |
| Source Sets | University of Arizona |
| Language | English |
| Detected Language | English |
| Type | text, Electronic Dissertation |
| 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. |
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