September 18, 2006
Robert Lipshitz (Columbia):
Q Gradings in Heegaard-Floer Homology
Abstract:
Heegaard-Floer homology, introduced by P. Ozsvath and Z. Szabo around
the turn of the century, applies holomorphic curve techniques to
low-dimensional topology. After recalling the definition (or
definitions) of Heegaard-Floer homology, we will give two constructions
of a relative Q gradings on the chain complex. The first, due to
Ozsvath-Szabo, uses maps induced by cobordisms. The second, which is
joint work of Dan Lee and the speaker, uses covering spaces. Time
permitting, we will outline a proof of the equivalence of the two
constructions. We will conclude with some wild speculation about
possible generalizations.
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