A. Yu. Morozov, “Are there $p$-adic knot invariants?”, TMF, 187:1 (2016), 3–11; Theoret. and Math. Phys., 187:1 (2016), 447

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Teoreticheskaya i Matematicheskaya Fizika, 2016, Volume 187, Number 1, Pages 3–11
DOI: https://doi.org/10.4213/tmf9047 (Mi tmf9047)

This article is cited in 18 scientific papers (total in 18 papers)

Are there

p

$p$ -adic knot invariants?

A. Yu. Morozov^abc

^a 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

Full-text PDF (452 kB) Citations (18)

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DOI: https://doi.org/10.4213/tmf9047

Abstract: We suggest using the Hall–Littlewood version of the Rosso–Jones formula to define the germs of

p

$p$ -adic HOMFLY-PT polynomials for torus knots

[m, n]

$[m,n]$ as coefficients of superpolynomials in a

q

$q$ -expansion. In this form, they have at least the

[m, n] \leftrightarrow [n, m]

$[m,n]\leftrightarrow[n,m]$ topological invariance. This opens a new possibility to interpret superpolynomials as

p

$p$ -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

$p$ -adic analysis,

p

$p$ -adic string.

Funding agency	Grant number
Russian Science Foundation	14-50-00150
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)

Received: 18.09.2015

English version:
Theoretical and Mathematical Physics, 2016, Volume 187, Issue 1, Pages 447–454
DOI: https://doi.org/10.1134/S0040577916040012

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: A. Yu. Morozov, “Are there

p

$p$ -adic knot invariants?”, TMF, 187:1 (2016), 3–11; Theoret. and Math. Phys., 187:1 (2016), 447–454

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf9047

https://doi.org/10.4213/tmf9047

https://www.mathnet.ru/eng/tmf/v187/i1/p3

This publication is cited in the following 18 articles:

E. Lanina, A. Morozov, “Defect and degree of the Alexander polynomial”, Eur. Phys. J. C, 82:11 (2022)
A. Yu. Morozov, “KNTZ trick from arborescent calculus and the structure of differential expansion”, Theoret. and Math. Phys., 204:2 (2020), 993–1019
L. Bishler, A. Morozov, “Perspectives of differential expansion”, Phys. Lett. B, 808 (2020), 135639
A. Morozov, “Pentad and triangular structures behind the Racah matrices”, Eur. Phys. J. Plus, 135:2 (2020)
A. Morozov, “On exclusive Racah matrices (s)over-bar for rectangular representations”, Phys. Lett. B, 793 (2019), 116–125
A. Morozov, “Extension of kntz trick to non-rectangular representations”, Phys. Lett. B, 793 (2019), 464–468
A. Anokhina, A. Morozov, A. Popolitov, “Nimble evolution for pretzel khovanov polynomials”, Eur. Phys. J. C, 79:10 (2019)
A. Morozov, “Generalized hypergeometric series for Racah matrices in rectangular representations”, Mod. Phys. Lett. A, 33:4 (2018), 1850020
A. Morozov, “Homfly for twist knots and exclusive Racah matrices inrepresentation [333]”, Phys. Lett. B, 778 (2018), 426–434
A. Morozov, “Factorization of differential expansion for non-rectangular representations”, Mod. Phys. Lett. A, 33:12 (2018), 1850062
A. Anokhina, A. Morozov, “Are Khovanov-Rozansky polynomials consistent with evolution in the space of knots?”, J. High Energy Phys., 2018, no. 4, 066
A. Morozov, “Knot polynomials for twist satellites”, Phys. Lett. B, 782 (2018), 104–111
A. Morozov, “On moduli space of symmetric orthogonal matrices and exclusive Racah matrix $\overline S$ for representation $R = [3,1]$ with multiplicities”, Phys. Lett. B, 766 (2017), 291–300
Ya. A. Kononov, A. Yu. Morozov, “Rectangular superpolynomials for the figure-eight knot $4_1$ ”, Theoret. and Math. Phys., 193:2 (2017), 1630–1646
B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, E. I. Zelenov, “ $p$ -Adic mathematical physics: the first 30 years”, p-Adic Numbers Ultrametric Anal. Appl., 9:2 (2017), 87–121
Ya. Kononov, A. Morozov, “On rectangular HOMFLY for twist knots”, Mod. Phys. Lett. A, 31:38 (2016), 1650223
A. Morozov, “Differential expansion and rectangular HOMFLY for the figure eight knot”, Nucl. Phys. B, 911 (2016), 582–605
A. Mironov, A. Morozov, A. Morozov, A. Sleptsov, “HOMFLY polynomials in representation [3, 1] for 3-strand braids”, J. High Energy Phys., 2016, no. 9, 134

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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