April 6, 2007

Nadya Shirokova (Stanford)

Title: On the classification of Floer-type theories

Abstract: Many Floer-type theories can be considered as categorifications of classical invariants. We propose a program of classification of such theories. We construct Floer-type local systems on the spaces of manifolds (including singular ones), extend them to the singular locus and introduce the definition of a local system of finite type. Our main examples come from Khovanov and Ozsvath-Szabo theories.