Time：17:00-19:00 （Beijing Time） July 08 ，2020
Title： Perverse sheaves and knot contact homology
Abstract:A knot is an oriented closed connected smooth curve in R3 . A general curve with possibly many components is called a link. One of the fundamental problems in topology is to classify knots by suitable invariants. In this talk we present a universal construction, called homotopy braid closure, that produces invariants of links in R3 starting with a braid group action on objects of a (model) category. Applying this construction to the natural action of the braid group Bn on the category of perverse sheaves on the two-dimensional disk with singularities at n marked points, we obtain a differential graded (DG) category that gives knot contact homology in the sense of L. Ng. As an application, we show that the category of finite-dimensional modules over the 0-th homology of this DG category is equivalent to the category of perverse sheaves on R3 with singularities at most along the link. [This is joint work with Yu. Berest and Wai-kit Yeung]
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