Caltech Geometry and Topology SeminarOctober 14th, 2009
Knot theory and quasi-morphisms
Michael Brandenbursky, Technion
Abstract: Quasi-morphisms on a group are real-valued functions which satisfy the homomorphism equation "up to a bounded error". They are known to be a helpful tool in the study of the algebraic structure of non-Abelian groups.

I will discuss a construction relating
a) certain knot and link invariants -in particular, the ones that come from the knot Floer homology and a Khovanov-type homology,
b) braid groups,
c) the dynamics of area-preserving diffeomorphisms of a two-dimensional disc,
d) quasi-morphisms on the group of all such compactly supported diffeomorphisms of the disc.