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4:00 pm Monday, April 16, 2018 Topology Seminar: Compression bodies and their boundary hyperbolic structuresby Vinh Dang (Lone Star College) in HBH 427- In the first part of the talk, we show that the set of cusp shapes of hyperbolic tunnel number one manifolds is dense in the Teichmuller space of the torus. As a consequence, there are infinitely many hyperbolic tunnel number one manifolds with at most one exceptional Dehn filling. A similar result holds for tunnel number n manifolds. This is in contrast to large volume Berge knots, which are tunnel number one manifolds, but with cusp shapes converging to a single point in Teichmuller space. In the second part, we describe some properties of the space of hyperbolic structures on the compression body C with genus 2 positive boundary and genus 1 negative boundary which are comparable to that of the punctured-torus. These compression bodies are fundamental objects used in the results in the first part.
Submitted by neil.fullarton@rice.edu |