# sl3–foam homology calculations

```@article{Lewark2012sl3foamHC,
title={sl3–foam homology calculations},
author={Lukas Lewark},
journal={Algebraic \& Geometric Topology},
year={2012},
volume={13},
pages={3661-3686}
}```
• 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…
12 Citations

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