**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.