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.
Mohamed Elhamdadi, Mustafa Hajij
University of South Florida, University of South Florida
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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