Geometry and Topology Seminar

Suppose K is a fibred knot in a 3-manifold M giving an open book decomposition of M, and that the supported contact structure ξ on M is overtwisted. Under what conditions do negative surgeries on K (considered as a transverse knot) result in a tight contact manifold? This problem becomes tractable when we replace the word "tight" with "having non-vanishing Heegaard Floer invariant", and we can find necessary and sufficient conditions for this. This will lead us to corollaries regarding L-space knots, the support genus of contact structures, and the support genus of Legendrian knots.