Berge duals and universally tight contact structures

Geometry Topology Seminar
Monday, April 2, 2012 - 14:00
1 hour (actually 50 minutes)
Skiles 005
Duke University
Berge has a construction that produces knots in S^3 that admit a lens space surgery. Conjecturally, his construction produces all such knots. This talk will consider knots that have such a surgery, and some of their contact geometric properties. In particular, knots in S^3 with a lens space surgery are fibered, and they all support the tight contact structure on S^3. From recent work of Hedden and Plamenevskaya, we also know that the dual to a lens space surgery on such a knot supports a tight contact structure on the resulting lens space. We consider the knots that are dual to Berge's knots, and we investigate whether the tight contact structure they support is a universally tight structure. Our results indicate a relationship between supporting this universally tight structure and being dual to a torus knot.