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arXiv · 2007.12532

Distinguishing Mutant Knots

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

Knot theory is actively studied both by physicists and mathematicians as it provides a connecting centerpiece for many physical and mathematical theories. One of the challenging problems in knot theory is distinguishing mutant knots. Mutant knots are not distinguished by colored HOMFLY-PT polynomials for knots colored by either symmetric and or antisymmetric representations of $SU(N)$. Some of the mutant knots can be distinguished by the simplest non-symmetric representation $[2,1]$. However there is a class of mutant knots which require more complex representations like $[4,2]$. In this paper we calculate polynomials and differences for the mutant knot polynomials in representations $[3,1]$ and $[4,2]$ and study their properties.

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L. Bishler, Saswati Dhara, T. Grigoryev, A. Mironov, A. Morozov, An. Morozov, P. Ramadevi, Vivek Kumar Singh, A. Sleptsov. 2020-07-24. Distinguishing Mutant Knots. https://doi.org/10.1016/j.geomphys.2020.103928

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