On the quantum filtration of the universal sl(2) foam cohomology

Details On the quantum filtration of the universal sl(2) foam cohomology On the quantum filtration of the universal sl(2) foam cohomology

2010-06-14

arxiv.org/abs/1006.2575v3

Journal of Knot Theory and its Ramifications, Volume 21, Issue 3 (March 2012)

Mathematics

Geometric Topology

10 pages, many figures; typos corrected and some changes made in the exposition at referee's suggestions

Scientific paper

10.1142/S0218216511009595

We investigate the filtered theory corresponding to the universal sl(2) foam cohomology $H_{a,h}$ for links, where a and h are complex numbers. We show that there is a spectral sequence converging to $H_{a,h}$ which is invariant under the Reidemeister moves, and whose E1 term is isomorphic to Khovanov homology. This spectral sequence can be used to obtain from the foam perspective an analogue of the Rasmussen invariant and a lower bound for the slice genus of a knot.

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