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Geometry and Topology Seminar

Friday, May 23, 2014
3:00pm to 5:00pm
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Plane Floer Homology and the Knot Concordance Group
Aliakbar Daemi, Grad Student, Mathematics, Harvard University,

Plane Floer homology defines a functor from the category of
3-manifolds and cobordisms to the category of vector spaces over an
appropriate Novikov ring. This homology theory admits a surgery exact
triangle or more generally an iterated version of the surgery exact
triangle in the form of a surgery cube. As a corollary, for a classical
link we derive a spectral sequence whose second page is a suitable version
of odd Khovanov homology and it abuts to the plane Floer homology of the
double cover of S^3 branched along the link. Another important property of
plane Floer homology is that it can be easily computed. We exploit this
fact and define a family of knot concordance invariants.

For more information, please contact Subhojoy Gupta by email at mathinfo@caltech.edu.