# One question about "Khovanov-Rozansky Homology and Topological Strings"

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In  "Khovanov-Rozansky Homology and Topological Strings" (http://lanl.arxiv.org/pdf/hep-th/0412243) a conjecture involving the  Poincaré-Khovanov-Rozansky polynomial of knots  and the BPS states in topological strings is formulated.  According with such conjecture the following results are obtained for the trefoil knot

I am conjecturing the next invariant as

My question: is such invariant correct?

asked Jan 21, 2018
edited Jan 23, 2018

perhaps $q^{15}$ missing ... Did you done the long calculus by hand ? It's more clear for me to try web cobordisms with some recursive algo

@igael , you are right, $q^{15}$ was missing. It was fixed.  Many thanks.

@Juancho : yes, according to the author, it is just the application of 1.8 and 4.7. But this doesn't answer the question. The document doesn't include the demonstration, it is only a strong indication for a further study. Remarkable observation ...

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