Duke Mathematical Journal

Khovanov-Rozansky homology of two-bridge knots and links

Jacob Rasmussen

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We compute the reduced version of Khovanov and Rozansky's sl(N) homology for two-bridge knots and links. The answer is expressed in terms of the skein polynomial of Hoste, Ocneanu, Millett, Freyd, Lickorish, and Yetter (or HOMFLY polynomial; see [6]) and signature

Article information

Duke Math. J., Volume 136, Number 3 (2007), 551-583.

First available in Project Euclid: 29 January 2007

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Zentralblatt MATH identifier

Primary: 57M27: Invariants of knots and 3-manifolds


Rasmussen, Jacob. Khovanov-Rozansky homology of two-bridge knots and links. Duke Math. J. 136 (2007), no. 3, 551--583. doi:10.1215/S0012-7094-07-13635-4. https://projecteuclid.org/euclid.dmj/1170084898

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  • D. Bar-Natan, On Khovanov's categorification of the Jones polynomial, Algebr. Geom. Topol. 2 (2002), 337--370.
  • —, FastKh in Mathematica package KnotTheory\`, \href{http://katlas.math.toronto.edu/wiki/Khovanov{\
  • J. S. Carter and M. Saito, Reidemeister moves for surface isotopies and their interpretation as moves to movies, J. Knot Theory Ramifications 2 (1993), 251--284.
  • J. H. Conway, ``An enumeration of knots and links, and some of their algebraic properties'' in Computational Problems in Abstract Algebra (Oxford, 1967), Pergamon, Oxford, 1970, 329--358.
  • N. M. Dunfield, S. Gukov, and J. Rasmussen, The superpolynomial for knot homologies, Experiment. Math. 15 (2006), 129--159.
  • P. Freyd, D. Yetter, J. Hoste, W. B. R. Lickorish, K. Millett, and A. Ocneanu, A new polynomial invariant of knots and links, Bull. Amer. Math. Soc. (N.S.) 12 (1985), 239--246.
  • B. Gornik, Note on Khovanov link cohomology, preprint.
  • J. Green, JavaKh in Mathematica package KnotTheory\`, \href{http://katlas.math.toronto.edu/wiki/Khovanov{\
  • J. Hoste and M. Thistlethwaite, Knotscape, www.math.utk.edu/$\sim$morwen/knotscape.html
  • V. F. R. Jones, On knot invariants related to some statistical mechanical models, Pacific. J. Math. 137 (1989), 311--334.
  • M. Khovanov, A categorification of the Jones polynomial, Duke Math. J. 101 (2000), 359--426.
  • —, Patterns in knot cohomology, I, Experiment. Math. 12 (2003), 365--374.
  • M. Khovanov and L. Rozansky, Matrix factorizations and link homology, preprint.
  • —, Matrix factorizations and link homology, II, preprint.
  • E. S. Lee, The support of Khovanov's invariants for alternating knots, preprint.
  • H. Murakami, T. Ohtsuki, and S. Yamada, Homfly polynomial via an invariant of colored plane graphs, Enseign. Math. (2) 44 (1998), 325--360.
  • K. Murasugi, Knot Theory and Its Applications, Birkhäuser, Boston, 1996.
  • J. Rasmussen, Khovanov homology and the slice genus, preprint.
  • A. Shumakovitch, KhoHo, www.geometrie.ch/KhoHo/
  • V. G. Turaev, The Yang-Baxter equation and invariants of links, Invent. Math. 92 (1988), 527--553.