Plane Floer Homology and Knot Concordance Group

Plane Floer Homology and Knot Concordance Group

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Ali Akbar Daemi, Harvard University
Fine Hall 314

Plane Floer Homology defines a functor from the category of 3-manifolds and cobordisms to the category of vector spaces over an appropriate Novikov field N. Like other Floer homologies assigned to 3-manifolds, this homology theory carries one important property, i.e., surgery exact triangle or more generally ``cubical surgery relation''. As a result, for a classical link we derive a spectral sequence whose second page is a suitable variant of Khovanov homology and it abuts to the plane floer homology of the double cover of S^3 branched along the link. Moreover, plane Floer homology can be easily computed. As an application we will show how to define a family of knot concordance invariants.