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Combinatorial Tangle Floer homology

Presented by: 
Vera Vertesi University of Strasbourg, CNRS (Centre national de la recherche scientifique)
Date: 
Friday 19th May 2017 - 13:30 to 14:30
Venue: 
INI Seminar Room 2
Abstract: 
Knot Floer homology is an invariant for knots and links defined by Ozsv\'ath and Szab\'o and independently by Rasmussen. It has proven to be a powerful invariant e.g. in computing the genus of a knot, or determining whether a knot is fibered. In this talk I define a generalisation of knot Floer homology for tangles; Tangle Floer homology is an invariant of tangles in D^3, $S^2xI or in S^3. Tangle Floer homology satisfies a gluing theorem and its version in S^3 gives back a stabilisation of knot Floer homology. Finally, I will discuss how to see tangle Floer homology as a categorification of the Reshetikhin-Turaev invariant for gl(1|1).

This is a joint work with I. Petkova and A. P. Ellis.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons