In this talk, I will present a universal construction, called homotopy braid closure, that produces
invariants of links in R^3 starting with a braid group action on objects of a (model) category C.
Applying this construction to the natural action of the braid group B_n 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 R^3 with singularities at most along the link.
[This is joint work with Yu. Berest and A. Eshmatov.]