Inventiones mathematicae

, Volume 182, Issue 2, pp 419–447 | Cite as

Khovanov homology and the slice genus

  • Jacob RasmussenEmail author


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 smooth slice genus of K. As a corollary, we give a purely combinatorial proof of the Milnor conjecture.


Spectral Sequence Short Exact Sequence Jones Polynomial Planar Diagram Floer Homology 
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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Dept. of MathematicsPrinceton UniversityPrincetonUSA
  2. 2.DPMMSUniversity of CambridgeCambridgeUK

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