# University of Toronto's Symplectic Geometry Seminar

Oct. 21 2002, 3:10 - 4

SS5017A

## Mikhail Khovanov

###
U.C.Davis

##
"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!