【数学学院】Perverse sheaves and knot contact homology

报告题目:Perverse sheaves and knot contact homology

报告人：Alimjon Eshmatov

报告人单位：University of Toledo

报告时间：6月28日（周四）下午16:00

报告地点：数学学院东409报告厅

邀请人：张斌

摘要：

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 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]