Geometry and Topology Seminar

Heegaard Floer contact invariants for positive rational surgery

Tom Mark, Associate Professor, Mathematics, University of Virginia,

Motivated by the existence question for tight contact structures

on 3-manifolds, I'll present a naturality result for the contact invariant

in Heegaard Floer theory for contact structures obtained by rational

contact surgery on a Legendrian knot with surgery coefficient at least 1.

As a consequence we obtain nonvanishing results for the contact invariant,

and hence tightness of the corresponding contact structure, in certain

previously unknown cases. This refines and extends a variety of results in

the literature, due variously to Golla, Lisca, and Stipsicz. A key

ingredient in the proof is a not-so-obvious generalization of Baldwin's

theorem on "capping off" to certain open books with monodromy that fixes a

nontrivial separating curve.

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For more information, please contact Yi Ni by email at [email protected].