Note on Khovanov link cohomology
Bojan Gornik
TL;DR
This paper generalizes Lee's results on sl(2) Khovanov cohomology to the sl(n) case, providing a filtered chain complex with a spectral sequence converging to cohomology depending only on linking numbers.
Contribution
It introduces a filtered chain complex for sl(n) Khovanov cohomology and computes its cohomology based solely on linking numbers of sublinks.
Findings
Spectral sequence E_2 term equals Khovanov cohomology
Cohomology depends only on linking numbers of sublinks
Extension of Lee's results to general sl(n) case
Abstract
We extend Lee's result on sl(2) Khovanov cohomology of a link L to the general sl(n) case: a filtered chain complex C(L) whose spectral sequence E_2 term equals Khovanov cohomology is exhibited. We also compute C(L)'s cohomology: it depends only on linking numbers of certain sublinks of L.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics