Heegaard Floer homology and knots
Monday January 28, 2008
01:30PM - 02:30PM
Speakers:
Peter Ozsvath
Abstract:
Heegaard Floer homology is an invariant for low-dimensional manifolds defined using Heegaard diagrams and holomorphic disks, constructed in joint work with Zolt{\'a}n Szab{\'o}. These constructions can be specialized to give an invariant for knots in the three-sphere, knot Floer homology, which has the structure of a bigraded Abelian group whose graded Euler characteristic is the Alexander polynomial. Unlike the Alexander polynomial, however, knot Floer homology contains precise geometric information about the knot:
it encodes the knot genus. I will discuss applications of this theory, as well as several recent advances in explicitly calculating these invariants in elementary terms. I will describe joint work with collaborators including Ciprian Manolescu, Sucharit Sarkar, Andr{\'a}s Stipsicz, Zoltan Szab{\'o}, and Dylan Thurston.
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