The Categorification of Vassiliev Theory

HOMOLOGICAL MIRROR SYMMETRY
Topic:The Categorification of Vassiliev Theory
Speaker:Nadya Shirokova
Affiliation:Stanford University
Date:Monday, April 2
Time/Room:2:00pm - 3:00pm/S-101

Many Floer-type theories are the categorifications of classical invariants. We describe a program of classification of such theories: we consider them as local systems on the spaces of manifolds that we constructed and extend them to the singular locus. We introduce the definition of the theory of finite type. Our main examples come from the Khovanov and Ozsvath-Szabo theories. In paricular we show that Khovanov local system, restricted to the subcategory of knots of the crossing number at most n is the theory of type n.