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Khovanov-Rozansky Homology and Topological Strings

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arxiv hep-th/0412243 v3 pith:VZ3S32WC submitted 2004-12-20 hep-th math.GT

Khovanov-Rozansky Homology and Topological Strings

classification hep-th math.GT
keywords homologyknottopologicalconjecturegroupsstringsapproachcaptured
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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We conjecture a relation between the sl(N) knot homology, recently introduced by Khovanov and Rozansky, and the spectrum of BPS states captured by open topological strings. This conjecture leads to new regularities among the sl(N) knot homology groups and suggests that they can be interpreted directly in topological string theory. We use this approach in various examples to predict the sl(N) knot homology groups for all values of N. We verify that our predictions pass some non-trivial checks.

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  1. Reductions in Khovanov-Rozansky operator formalism

    hep-th 2026-05 unverdicted novelty 7.0

    Khovanov-Rozansky invariants are recast as a bicomplex of local operators D and conjugations χ^(±), with nilpotency on closed diagrams allowing reductions that simplify the hypercube construction.