sl3–foam homology calculations

  title={sl3–foam homology calculations},
  author={Lukas Lewark},
  journal={Algebraic \& Geometric Topology},
  • Lukas Lewark
  • Published 11 December 2012
  • Mathematics
  • Algebraic & Geometric Topology
We exhibit a certain infinite family of three-stranded quasi-alternating pretzel knots, which are counterexamples to Lobb’s conjecture that the sl3 ‐knot concordance invariant s3 (suitably normalised) should be equal to the Rasmussen invariant s2 . For this family,js3j js2j. The main tool is an implementation of Morrison and Nieh’s algorithm to calculate Khovanov’s sl3 ‐foam link homology. Our C++ program is fast enough to calculate the integral homology of, eg, the .6;5/‐torus knot in six… 

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