Foundations of the colored Jones polynomial of singular knots
Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 937-956
https://doi.org/10.4134/BKMS.b170403
Published online May 31, 2018
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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