Title: On the classification of Floer-type theories
Speaker: Professor Nadya Shirokova
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Abstract:
Many Floer-type theories can be considered as categorifications of classical invariants. We outline a program of classification of such theories. We construct the local systems of Floer complexes 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. We show that the Khovanov local system, restricted to the subcategory of knots of the crossing number at most n is a theory of finite type n. We also have examples in Ozsvath-Szabo theory (arXiv:0704.1330).Date: Thursday, May 31, 2007