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TQFT structures in link Floer homology

Banff International Research Station for Mathematical Innovation and Discovery

We will discuss a TQFT for the full link Floer complex, involving decorated link cobordisms. It is inspired by Juhasz's TQFT for sutured Floer homology. We will discuss how the TQFT recovers standard bounds on concordance invariants like Ozsvath and Szabo's tau invariant and Rasmussen's local h invariants (which are normally proven using surgery theory) and also gives a new bound on Upsilon. We will also see how well known maps in the link Floer complex can be encoded into decorations on surfaces, and as an example we will see how Sarkar's formula for a mapping class group action on link Floer homology is recovered by some simple pictorial relations. Time permitting, we will also discuss how these pictorial relations give a connected sum formula for Hendricks and Manolescu's involutive invariants for knot Floer homology.

Mathematics; Manifolds and cell complexes; Differential geometry; Low dimensional topology

video/mp4

Author affiliation: UCLA

2018-01-28

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/64468

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/