Tianyuan Mathematical Center
in Southwest China

Perverse sheaves and knot contact homology

[Math. Dept.]

June 28, 2018  16:00-17:00

E409  School of Mathematics

SPEAKER

Alimjon Eshmatov (University of Toledo)

ABSTRCT

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]

SUPPORTED BY

Tianyuan Mathematical Center in Southwest China

School of Mathematics, Sichuan University