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

2010/11/09 by Lev Rozansky, Rozansky, Lev · 4 citations
Mathematics · Physics and Astronomy · #57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Geometry and complex manifolds #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.1011.1958

openalex publication_date 2010/11/09 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

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.

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