A categorification of the stable SU(2) Witten-Reshetikhin-Turaev invariant of links in S2 x S1.

Authors: Lev Rozansky
Subjects: Geometric Topology
link: http://arxiv.org/abs/1011.1958
Abstract

The WRT invariant of a link L in S2xS1 at sufficiently high values of the
level r can be expresses as an evaluation of a special polynomial invariant of
L at 2r-th root of unity. We categorify this polynomial invariant by
associating to L a bigraded homology whose graded Euler characteristic is equal
to this polynomial. If L is presented as a closure of a tangle in S2xS1, then
the homology of L is defined as the Hochschild homology of the H_n-bimodule
associated to the tangle by M. Khovanov. This homology can also be expressed as
a stable limit of Khovanov homology of the circular closure of the tangle in S3
through the torus braid with high twist.