The Superpolynomial for Knot Homologies

@article{Dunfield2006TheSF,
  title={The Superpolynomial for Knot Homologies},
  author={Nathan M. Dunfield and Sergei Gukov and Jacob Rasmussen},
  journal={Experimental Mathematics},
  year={2006},
  volume={15},
  pages={129 - 159}
}
  • Nathan M. Dunfield, Sergei Gukov, Jacob Rasmussen
  • Published 2006
  • Mathematics, Physics, Computer Science
  • Experimental Mathematics
  • We propose a framework for unifying the sl(N) Khovanov– Rozansky homology (for all N) with the knot Floer homology. We argue that this unification should be accomplished by a triply graded homology theory that categorifies the HOMFLY polynomial. Moreover, this theory should have an additional formal structure of a family of differentials. Roughly speaking, the triply graded theory by itself captures the large-N behavior of the sl(N) homology, and differentials capture nonstable behavior for… CONTINUE READING

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