Khovanov homology and the slice genus

Abstract

We use Lee's work on the Khovanov homology to define a knot invariant s. We show that s(K) is a concordance invariant and that it provides a lower bound for the slice genus of K. As a corollary, we give a purely combinatorial proof of the Milnor conjecture.

20 pages, 8 figures

References in corpus (6)

• Floer homology and knot complements
• Knot Floer homology and the four-ball genus
• Heegaard Floer homology and alternating knots
• The support of the Khovanov's invariants for alternating knots
• Knot Floer homology, genus bounds, and mutation
• Holomorphic disks and knot invariants

Cited by in corpus (20)

• Khovanov's homology for tangles and cobordisms
• Holomorphic disks and link invariants
• Legendrian knots, transverse knots and combinatorial Floer homology
• A slice genus lower bound from sl(n) Khovanov-Rozansky homology
• Khovanov homology, sutured Floer homology, and annular links
• Open-closed TQFTs extend Khovanov homology from links to tangles
• Five Lectures on Khovanov Homology
• Khovanov's invariant for closed surfaces
• Khovanov-Rozansky homology of two-bridge knots and links
• An invariant of link cobordisms from symplectic Khovanov homology
• Khovanov homology, open books, and tight contact structures
• A concordance invariant from the Floer homology of double branched covers
• Unknotting sequences for torus knots
• The Universal sl_2 Link Homology Theory
• Concordance invariants from higher order covers
• A spanning tree model for Khovanov homology
• Khovanov-Rozansky Homology and Conway Mutation
• A categorification of the quantum sl(N)-link polynomials using foams
• Order in the concordance group and Heegaard Floer homology
• Slice knots with distinct Ozsvath-Szabo and Rasmussen Invariants