Large color $R$-matrix for knot complements and strange identities

Sunghyuk Park

doi:10.1142/s0218216520500972

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arXiv · 2004.02087

Large color $R$-matrix for knot complements and strange identities

Sunghyuk Park

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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.

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BibTeX RIS

Sunghyuk Park. 2020-04-05. Large color $R$-matrix for knot complements and strange identities. https://doi.org/10.1142/s0218216520500972

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