Bumping in the Deformation Spaces of Hyperbolic 3-Manifolds with Compressible Boundary.
dc.contributor.author | Renardy, David | |
dc.date.accessioned | 2016-09-13T13:50:12Z | |
dc.date.available | NO_RESTRICTION | |
dc.date.available | 2016-09-13T13:50:12Z | |
dc.date.issued | 2016 | |
dc.date.submitted | 2016 | |
dc.identifier.uri | https://hdl.handle.net/2027.42/133206 | |
dc.description.abstract | Let M be a compact, hyperbolizable 3-manifold with boundary and let AH(M) denote the space of discrete faithful representations of the fundamental group of $M$ into the group of orientation preserving isometries of hyperbolic 3-space. The components of the interior of AH(M) are well understood, with components enumerated by the space of marked homeomorphism types of oriented, compact irreducible 3-manifolds homotopy equivalent to M. When M has incompressible boundary, Anderson, Canary and McCullough characterized precisely when two components of the interior of AH(M) ``bump'', that is, when they have intersecting closures in AH(M). We introduce a construction that provides examples of bumping in the case when M has compressible boundary. Specifically, we exhibit bumping between components when the change in marked homeomorphism type corresponds to ``shuffling'' one end of an attached one handle around components of the boundary of M bordering a primitive essential annulus. | |
dc.language.iso | en_US | |
dc.subject | Kleinian Groups | |
dc.subject | Hyperbolic 3-manifolds | |
dc.title | Bumping in the Deformation Spaces of Hyperbolic 3-Manifolds with Compressible Boundary. | |
dc.type | Thesis | en_US |
dc.description.thesisdegreename | PhD | |
dc.description.thesisdegreediscipline | Mathematics | |
dc.description.thesisdegreegrantor | University of Michigan, Horace H. Rackham School of Graduate Studies | |
dc.contributor.committeemember | Canary, Richard D | |
dc.contributor.committeemember | Goldberg, Deborah E | |
dc.contributor.committeemember | Spatzier, Ralf J | |
dc.contributor.committeemember | Scott, G Peter | |
dc.contributor.committeemember | Koch, Sarah Colleen | |
dc.subject.hlbsecondlevel | Mathematics | |
dc.subject.hlbtoplevel | Science | |
dc.description.bitstreamurl | http://deepblue.lib.umich.edu/bitstream/2027.42/133206/1/drenardy_1.pdf | |
dc.owningcollname | Dissertations and Theses (Ph.D. and Master's) |
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