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Geometry and Topology Seminar

Friday, November 19, 2021
3:00pm to 4:00pm
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Linde Hall 187
Floer Homology and quasipositive surfaces
Lev Tovstopyat-Nelip, Department of Mathematics, Michigan State University,

Ozsvath and Szabo have shown that knot Floer homology detects knot genus - the largest Alexander grading of a non-trivial homology class is equal to the genus.

We give a new contact geometric interpretation of this fact by realizing such a class via the transverse knot invariant introduced by Lisca, Ozsvath, Stipsicz and Szabo. Our approach relies on the "convex decomposition theory" of Honda, Kazez and Matic - a contact geometric interpretation of Gabai's sutured hierarchies.

We use this new interpretation to study the "next-to-top" summand of knot Floer homology, and to show that Heegaard Floer homology detects quasi-positive Seifert surfaces. Some of this talk represents joint work with Matthew Hedden.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit https://sites.google.com/site/caltechgtseminar/home.