## Topology Seminar (Main Talk): Tight Contact Structures via Admissible Transverse Surgery

Seminar | February 8 | 4:10-5 p.m. | 3 Evans Hall

James Conway, UC Berkeley

Department of Mathematics

Suppose $K$ is a fibred knot in a 3-manifold $M$ giving an open book decomposition of $M$, and that the supported contact structure $\xi _K$ on $M$ is overtwisted. Under what conditions does negative surgeries on $K$ (considered as a transverse knot in $(M, \xi _K)$) result in a tight contact manifold?

This problem becomes tractable when we strengthen the requirements of the surgered manifold to be one with non-vanishing Heegaard Floer invariants, and we can get necessary and sufficient conditions. The result also leads us to several corollaries regarding L-space knots, the support genus of contact structures, and the support genus of Legendrian knots.

hongbins@berkeley.edu