Concordance maps in knot Floer homology

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• Marco Marengon, Imperial
• Wednesday 25 May 2016, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Ivan Smith.

Knot Floer homology (HFK) is a bi-graded vector space, which is an invariant of a knot in S3. Given a (decorated) knot concordance between two knots K and L (that is, an embedded annulus in S3 x [0,1] that K and L co-bound), Juhász defined a map between their knot Floer homologies. We prove that this map preserves the bigrading of HFK and is always non-zero. This has some interesting applications, in particular the existence of a non-zero element in HFK associated to each properly embedded disc in B4 whose boundary is the knot K in S3. This is joint work with András Juhász.

This talk is part of the Differential Geometry and Topology Seminar series.

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