A slice genus lower bound from sl(n) Khovanov–Rozansky homology

2007/02/13 by Andrew Lobb · 2 citations
Computer Science · Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Topological and Geometric Data Analysis #math.GT #msc:57M25

paper · pdf · doi:10.1016/j.aim.2009.06.001

published as Adv. Math. 222 (2009) 1220-1276 · 68 pages, 43 figures; unused figures removed

arxiv created 2007/02/13 · openalex publication_date 2009/06/28 · arxiv updated 2010/06/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show that perturbing the definition of sl(n) Khovanov-Rozansky link homology gives a lower bound on the slice genus of a knot. As a corollary this yields another proof of Milnor's conjecture on the slice genus of torus knots.

Citations

• Khovanov homology and the slice genus
• An endomorphism of the Khovanov invariant
• Matrix factorizations and link homology

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