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Matrix factorizations and link homology II

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arxiv math/0505056 v2 pith:HALUJPSH submitted 2005-05-03 math.QA math.GT

Mikhail Khovanov , Lev Rozansky This is my paper · ORCID
classification math.QAmath.GT
keywords linkcohomologycomplexassignbigradedbraidcharacteristicclosure
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To a presentation of an oriented link as the closure of a braid we assign a complex of bigraded vector spaces. The Euler characteristic of this complex (and of its triply-graded cohomology groups) is the HOMFLYPT polynomial of the link. We show that the dimension of each cohomology group is a link invariant.

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  1. Bipartite expansion beyond biparticity

    hep-th 2025-01 conditional novelty 6.0 of 10

    The authors construct positive decompositions of fundamental HOMFLY polynomials in variables φ, φ̄, D for arbitrary knots, not just bipartite ones, and give a criterion to detect when such a decomposition conceals a b...

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