Wall-Crossing Morphisms in Khovanov-Rozansky Homology

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.

11 pages, no figures

References in corpus (2)

• Some differentials on Khovanov-Rozansky homology
• On the classification of Floer-type theories