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

Understand

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.