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Overview of Knot Invariants at Roots of Unity

  • METHODS OF THEORETICAL PHYSICS
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We discuss different invariants of knots and links that depend on a primitive root of unity. We clarify the definitions of existing invariants with the Reshetikhin–Turaev method, present the generalization of ADO invariants to \({{\mathcal{U}}_{q}}(s{{l}_{N}})\) and highlight the connections between different invariants.

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ACKNOWLEDGMENTS

I am extremely grateful to my scientific advisors A. Mironov and An. Morozov for their guidance, patience and insight. I also thank V. Alexeev, T. Grigoryev, S. Mironov, A. Morozov, A. Sleptsov, and N. Tselousov for fruitful discussions.

Funding

This work was supported in part by the Russian Foundation for Basic Research, project no. 21-52-52004.

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Authors and Affiliations

  1. Lebedev Physics Institute, Russian Academy of Sciences, 119991, Moscow, Russia

    L. Bishler

  2. Institute for Information Transmission Problems, Russian Academy of Sciences, 127994, Moscow, Russia

    L. Bishler

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  1. L. Bishler
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Correspondence to L. Bishler.

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Bishler, L. Overview of Knot Invariants at Roots of Unity. Jetp Lett. 116, 185–191 (2022). https://doi.org/10.1134/S0021364022601294

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