New York Journal of Mathematics
Volume 22 (2016) 1439-1456

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Khaled Bataineh, Mohamed Elhamdadi, and Mustafa Hajij

The colored Jones polynomial of singular knots

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Published: December 1, 2016
Keywords: Skein theory, singular knots, colored Jones polynomial
Subject: 57M27
Abstract
We generalize the colored Jones polynomial to 4-valent graphs. This generalization is given as a sequence of invariants in which the first term is a one variable specialization of the Kauffman-Vogel polynomial. We use the invariant we construct to give a sequence of singular braid group representations.
Author information

Khaled Bataineh:
Department of Mathematics and Statistics, Jordan University of Science and Technology, Irbid 22110 Jordan
khaledb@just.edu.jo

Mohamed Elhamdadi:
Department of Mathematics, University of South Florida, Tampa, FL 33647 USA
emohamed@math.usf.edu

Mustafa Hajij:
Department of Mathematics, University of South Florida, Tampa, FL 33647 USA
mhajij@usf.edu