University of Toronto's Symplectic Geometry Seminar

Oct. 21 2002, 3:10 - 4

Mikhail Khovanov


"The first nontrivial example of a braid group action in a triangulated category"

Abstract: We construct a faithful braid group action in the homotopy category of complexes of modules over a certain finite dimensinal algebra A. Braids act by functors, and the action extends to a representation of the category of braid cobordisms, the latter acting by natural tranformations. Algebra A appears magically in algebraic geometry, the McKay correspondence, Floer homology, Hilbert schemes, and Hodge theory. Two alternative and less scary titles of this lecture: Modular representation theory of finite groups knows about four-dimensional topology! You can play with triangulated categories without knowing their definition!