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Are there p-adic knot invariants?

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Abstract

We suggest using the Hall–Littlewood version of the Rosso–Jones formula to define the germs of p-adic HOMFLY-PT polynomials for torus knots [m, n] as coefficients of superpolynomials in a q-expansion. In this form, they have at least the [m, n] ↔ [n, m] topological invariance. This opens a new possibility to interpret superpolynomials as p-adic deformations of HOMFLY polynomials and poses a question of generalizing to other knot families, which is a substantial problem for several branches of modern theory.

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Authors and Affiliations

  1. Institute for Theoretical and Experimental Physics, Moscow, Russia

    A. Yu. Morozov

  2. Kharkevich Institute for Information Transmission Problems, RAS, Moscow, Russia

    A. Yu. Morozov

  3. National Research Nuclear University MEPhI, Moscow, Russia

    A. Yu. Morozov

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Correspondence to A. Yu. Morozov.

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This work was performed at the Kharkevich Institute for Information Transmission Problems and was funded by the Russian Science Foundation (Grant No. 14-50-00150).

Prepared from an English manuscript submitted by the author; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 187, No. 1, pp. 3–11, April, 2016.

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Morozov, A.Y. Are there p-adic knot invariants?. Theor Math Phys 187, 447–454 (2016). https://doi.org/10.1134/S0040577916040012

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