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. |
Department of Mathematics, University of Oregon, Eugene OR 97403
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