Abstract

We study hyperbolic structures on the compression body C with genus 2 positive boundary and genus 1 negative boundary. We consider individual hyperbolic structures as well as special regions in the space of all such hyperbolic structures. We use some properties of the boundary hyperbolic structures on C to establish an interesting property of cusp shapes of tunnel number one manifolds. This extends a result of Nimershiem in [26] to the class of tunnel number one manifolds. We also establish convergence results on the geometry of compression bodies. This extends the work of Ito in [13] from the punctured-torus case to the compression body case.

Degree

PhD

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

http://lib.byu.edu/about/copyright/

Date Submitted

2015-12-01

Document Type

Dissertation

Handle

http://hdl.lib.byu.edu/1877/etd8180

Keywords

Hyperbolic Manifolds, Kleinian Groups, Compression Bodies

Included in

Mathematics Commons

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