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arXiv · 2004.06598

Difference of mutant knot invariants and their differential expansion

L. Bishler·Saswati Dhara·T. Grigoryev·A. Mironov·A. Morozov·An. Morozov·P. Ramadevi·Vivek Kumar Singh·A. Sleptsov
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Abstract

We evaluate the differences of HOMFLY-PT invariants for pairs of mutant knots colored with representations of $SL(N)$, which are large enough to distinguish between them. These mutant pairs include the pretzel mutants, which require at least the representation, labeled by the Young diagram $[4,2]$. We discuss the differential expansion for the differences, it is non-trivial in the case of mutants, which have the non-zero defect. The most effective technical tool, in this case, turns out to be the standard Reshetikhin-Turaev approach.

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L. Bishler, Saswati Dhara, T. Grigoryev, A. Mironov, A. Morozov, An. Morozov, P. Ramadevi, Vivek Kumar Singh, A. Sleptsov. 2020-04-14. Difference of mutant knot invariants and their differential expansion. https://doi.org/10.1134/s0021364020090015

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