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  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  from the punctured-torus case to the compression body case.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Dang, Vinh Xuan, "Compression Bodies and Their Boundary Hyperbolic Structures" (2015). Theses and Dissertations. 5662.
Hyperbolic Manifolds, Kleinian Groups, Compression Bodies