CaltechAUTHORS
  A Caltech Library Service

Large color R-matrix for knot complements and strange identities

Park, Sunghyuk (2020) Large color R-matrix for knot complements and strange identities. Journal of Knot Theory and its Ramifications, 29 (14). Art. No. 2050097. ISSN 0218-2165. https://resolver.caltech.edu/CaltechAUTHORS:20210305-103643058

[img] PDF - Accepted Version
See Usage Policy.

743Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20210305-103643058

Abstract

The Gukov–Manolescu series, denoted by F_K, is a conjectural invariant of knot complements that, in a sense, analytically continues the colored Jones polynomials. In this paper we use the large color R-matrix to study F_K for some simple links. Specifically, we give a definition of F_K for positive braid knots, and compute F_K for various knots and links. As a corollary, we present a class of “strange identities” for positive braid knots.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1142/s0218216520500972DOIArticle
https://arxiv.org/abs/2004.02087arXivDiscussion Paper
ORCID:
AuthorORCID
Park, Sunghyuk0000-0002-6132-0871
Additional Information:© 2020 World Scientific Publishing Co. Received 8 September 2020; Accepted 22 December 2020; Published: 20 January 2021. I would like to thank Sergei Gukov and Ciprian Manolescu for insightful discussions, as well as Piotr Kucharski, Robert Osburn, and Nikita Sopenko for useful conversations. The author was supported by Kwanjeong Educational Foundation.
Funders:
Funding AgencyGrant Number
Kwanjeong Educational FoundationUNSPECIFIED
Subject Keywords:R-matrix; Verma module; knot complement; q-series; colored Jones polynomial; strange identity
Issue or Number:14
Classification Code:AMSC: 57K16, 57K31, 16T25
Record Number:CaltechAUTHORS:20210305-103643058
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210305-103643058
Official Citation:Large color R-matrix for knot complements and strange identities. Sunghyuk Park. Journal of Knot Theory and Its Ramifications 2020 29:14; DOI: 10.1142/s0218216520500972
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108328
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Mar 2021 23:40
Last Modified:08 Mar 2021 23:40

Repository Staff Only: item control page