This thesis investigates various rigidity and flexibility phenomena of convex projective structures on hyperbolic manifolds, particularly in dimension 3. Let M[superscipt n] be a finite volume hyperbolic n-manifold where [mathematical equation] and [mathematical symbol] be its fundamental group. Mostow rigidity tells us that there is a unique conjugacy class of discrete faithful representation of [mathematical symbol] into PSO(subscript n, 1). In light of this fact we examine when this representations can be non-trivially deformed into the larger Lie group of PGL[subscript n+1](R) as well as the relationship between these deformations and convex projective structures on M. Specifically, we show that various two-bridge knots do not admit such deformations into PGL[subscript 4](R) satisfying certain boundary conditions. We subsequently use this result to show that certain orbifold surgeries on amphicheiral knot complements do admit deformations. / text
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/21681 |
| Date | 23 October 2013 |
| Creators | Ballas, Samuel Aaron |
| Source Sets | University of Texas |
| Language | en_US |
| Detected Language | English |
| Format | application/pdf |
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