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TMF, 2016, Volume 187, Number 1, Pages 3–11 (Mi tmf9047)  

This article is cited in 13 scientific papers (total in 13 papers)

Are there $p$-adic knot invariants?

A. Yu. Morozovabc

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

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

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)


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

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

Bibliographic databases:

Received: 18.09.2015

Citation: A. Yu. Morozov, “Are there $p$-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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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Ya. Kononov, A. Morozov, “On rectangular HOMFLY for twist knots”, Mod. Phys. Lett. A, 31:38 (2016), 1650223  crossref  mathscinet  zmath  isi  elib  scopus
    2. A. Morozov, “Differential expansion and rectangular HOMFLY for the figure eight knot”, Nucl. Phys. B, 911 (2016), 582–605  crossref  zmath  isi  elib  scopus
    3. 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  crossref  mathscinet  zmath  isi  scopus
    4. 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  crossref  isi  scopus
    5. Ya. A. Kononov, A. Yu. Morozov, “Rectangular superpolynomials for the figure-eight knot $4_1$”, Theoret. and Math. Phys., 193:2 (2017), 1630–1646  mathnet  crossref  crossref  adsnasa  isi  elib
    6. 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  crossref  mathscinet  zmath  isi  scopus
    7. A. Morozov, “Generalized hypergeometric series for Racah matrices in rectangular representations”, Mod. Phys. Lett. A, 33:4 (2018), 1850020  crossref  mathscinet  zmath  isi  scopus
    8. A. Morozov, “Homfly for twist knots and exclusive Racah matrices inrepresentation [333]”, Phys. Lett. B, 778 (2018), 426–434  crossref  zmath  isi  scopus
    9. A. Morozov, “Factorization of differential expansion for non-rectangular representations”, Mod. Phys. Lett. A, 33:12 (2018), 1850062  crossref  mathscinet  zmath  isi  scopus
    10. A. Anokhina, A. Morozov, “Are Khovanov-Rozansky polynomials consistent with evolution in the space of knots?”, J. High Energy Phys., 2018, no. 4, 066  crossref  mathscinet  isi  scopus
    11. A. Morozov, “Knot polynomials for twist satellites”, Phys. Lett. B, 782 (2018), 104–111  crossref  mathscinet  isi  scopus
    12. Morozov A., “On Exclusive Racah Matrices (S)Over-Bar For Rectangular Representations”, Phys. Lett. B, 793 (2019), 116–125  crossref  isi
    13. Morozov A., “Extension of Kntz Trick to Non-Rectangular Representations”, Phys. Lett. B, 793 (2019), 464–468  crossref  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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