An Algebraic Approach to Knot Floer Homology

When
Start: 10/04/2011 - 3:00pm
End  : 10/04/2011 - 4:00pm

Category
Topology Seminar

Speaker
Allison Gilmore, Princeton

Abstract

Ozsvath and Szabo gave the first completely algebraic description of knot Floer homology via a cube of resolutions construction. Starting with a braid diagram for a knot, one singularizes or smooths each crossing, then associates an algebra to each resulting singular braid. These can be arranged into a chain complex that computes knot Floer homology. After introducing knot Floer homology in general, I will explain this construction, then outline a fully algebraic proof of invariance for knot Floer homology that avoids any mention of holomorphic disks or grid diagrams. I will close by describing some potential applications of this algebraic approach to knot Floer homology, including potential connections with Khovanov-Rozansky's HOMFLY-PT homology.

Where
Millikan 211, Pomona College

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