Simplified Khovanov-Rozansky Chain Complexes of Open 2-braids

Details Simplified Khovanov-Rozansky Chain Complexes of Open 2-braids Simplified Khovanov-Rozansky Chain Complexes of Open 2-braids

2011-11-15

arxiv.org/abs/1111.3669v1

Mathematics

Geometric Topology

16 pages, 13 figures

Scientific paper

Motivated by the works of Krasner [arXiv:0801.4018] and Lobb [arXiv:1103.1412], we simplify the Khovanov-Rozansky chain complexes of open 2-braids. As an application, we show that, for a knot containing a "long" 2-braid, the sl(N) Rasmussen invariant of this knot depends linearly on the length of this 2-braid. We refine this result for (2,2k+1) cable knots and, as a simple corollary, compute the sl(2) Rasmussen invariants of (2,2k+1) cables of slice and amphicheiral knots.

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