Rogers-Ramanujan type identities for alternating knots

Abstract

We highlight the role of q-series techniques in proving identities arising from knot theory. In particular, we prove Rogers-Ramanujan type identities for alternating knots as conjectured by Garoufalidis, Le and Zagier.

26 pages, typos corrected, to appear in the Journal of Number Theory, Special Issue dedicated to Winnie Li

References in corpus (2)

• Rogers-Ramanujan type identities and the head and tail of the colored Jones polynomial
• Quantum Knot Invariants

Cited by in corpus (7)

• q-series and tails of colored Jones polynomials
• A $q$-series identity via the ${\mathfrak{sl}}_3$ colored Jones polynomials for the $(2,2m)$-torus link
• Coloured ${\mathfrak{sl}}_r$ invariants of torus knots and characters of ${\mathcal{W}}_r$ algebras
• Foundations of the Colored Jones Polynomial of singular knots
• Twist Regions and Coefficients Stability of the Colored Jones Polynomial
• The zero stability for the one-row colored ${\mathfrak{sl}}_3$ Jones polynomial
• On the Very-well-poised Bilateral Basic Hypergeometric ${}_5{\psi }_5$ Series