This article is cited in 18 papers

Are there $p$-adic knot invariants?

A. Yu. Morozov<sup>abc

a</sup> National Research Nuclear University MEPhI, Moscow, Russia
^b Institute for Theoretical and Experimental Physics, Moscow, Russia
^c Institute for Information Transmission Problems, RAS, Moscow, Russia

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 $[m,n]\leftrightarrow[n,m]$ 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.

Keywords: knot polynomial, $p$-adic analysis, $p$-adic string.

Received: 18.09.2015

DOI: 10.4213/tmf9047

 English version: Theoretical and Mathematical Physics, 2016, 187:1, 447–454

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