Wall-Crossing Morphisms in Khovanov-Rozansky Homology

2007/06/11 by Nadya Shirokova, Ben Webster, Shirokova, Nadya +1
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA #msc:57M25

paper · pdf · doi:10.48550/arxiv.0706.1388

11 pages, no figures

arxiv created 2007/06/11 · arxiv updated 2009/12/01

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 \mathfraksl_n quantum invariants.

Related

• Some differentials on Khovanov-Rozansky homology
• Crossing change on Khovanov homology and a categorified Vassiliev skein relation
• Khovanov-Rozansky homology of two-bridge knots and links
• Computations of HOMFLY homology
• Knot invariants arising from homological operations on Khovanov homology