Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2018; 55(3): 937-956

Online first article February 27, 2018      Printed May 31, 2018

https://doi.org/10.4134/BKMS.b170403

Copyright © The Korean Mathematical Society.

Foundations of the colored Jones polynomial of singular knots

Mohamed Elhamdadi, Mustafa Hajij

University of South Florida, University of South Florida

Abstract

This article gives the foundations of the colored Jones polynomial for singular knots. We extend Masbum and Vogel's algorithm \cite{MV} to compute the colored Jones polynomial for any singular knot. We also introduce the tail of the colored Jones polynomial of singular knots and use its stability properties to prove a false theta function identity that goes back to Ramanujan.

Keywords: colored Jones polynomials, singular knots, Ramanujan theta and false theta identities.

MSC numbers: 57M27, 57M25, 11P48

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