Swiss Knots 2011

Knot Theory and Algebra

Lake Thun, May 23-27

Elevating link homology theories and TQFT'es via infinite cyclic coverings

Prof. Dr. Oleg Viro's talk
Date: 27.05.11   Time: 09.00 - 09.50   Room: Gwatt Zentrum

Abstract: Using infinite cyclic coverings, we obtain from a link homology theory invariants of a collection of smooth surfaces generically immersed to the 4-sphere or to some other 4-manifolds. The invariants are bigraded Z[Z]-modules. A similar construction based on a (2+1)-TQFT instead of a link homology theory gives rise to an invariant of a classical link. The invariant is a Z[Z]-module which is a direct sum of submodules corresponding to colorings of meridians and longitudes of the link components. In the case of the TQFT based on the quantum sl2 at a root of unity, the value of the colored Jones polynomial of the link at the root of unity is recovered as a character of the module.