Wall-Crossing Morphisms in Khovanov-Rozansky Homology

Nadya Shirokova; Ben Webster

Wall-Crossing Morphisms in Khovanov-Rozansky Homology

Geometric Topology 2007-06-12 v1 Quantum Algebra

Authors: Nadya Shirokova , Ben Webster

Abstract

We define a wall-crossing morphism for Khovanov-Rozansky homology; that is, a map between the KR homology of knots related by a crossing change. Using this map, we extend KR homology to an invariant of singular knots categorifying the Vasilliev derivative of the HOMFLY polynomial, and of $\mathfrak{sl}_n$ quantum invariants.

Keywords

Khovanov-Rozansky homology wall-crossing morphism singular knots HOMFLY polynomial Vassiliev derivative quantum invariants

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@article{arxiv.0706.1388,
  title  = {Wall-Crossing Morphisms in Khovanov-Rozansky Homology},
  author = {Nadya Shirokova and Ben Webster},
  journal= {arXiv preprint arXiv:0706.1388},
  year   = {2007}
}

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11 pages, no figures

Wall-Crossing Morphisms in Khovanov-Rozansky Homology

Abstract

Keywords

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