Towards Catastrophe theory for Khovanov-Rozansky homology

Abstract

We briefly summarise our results on jumps in the analytic formulas for the Khovanov(-Rozansky) polynomials. We conclude from the empiric data that there are ``regular'' and ``weird'' catastrophes, which drastically differ by form of the associated jumps in the Khovanov(-Rozansky) polynomials. This is the first step towards the catastrophe theory for the cohomological knot invariants. In particular, it can be another way to see these quantities as observables in cohomological quantum field theory.

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Cited by in corpus (2)

• Khovanov--Rozansky matrix factorization reduction for bipartite links
• Operator lift of Reshetikhin-Turaev formalism to Khovanov-Rozansky TQFTs