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March 2012 $N$-degeneracy in rack homology and link invariants
Mohamed Elhamdadi, Sam Nelson
Hiroshima Math. J. 42(1): 127-142 (March 2012). DOI: 10.32917/hmj/1333113010

Abstract

The aim of this paper is to define a homology theory for racks with finite rank $N$ and use it to define invariants of knots generalizing the CJKLS 2-cocycle invariants related to the invariants defined in S. Nelson, Link invariants from finite racks, arXiv:0808.0029. For this purpose, we prove that $N$-degenerate chains form a sub-complex of the classical complex defining rack homology. If a rack has rack rank $N=1$ then it is a quandle and our homology theory coincides with the CKJLS homology theory. Nontrivial cocycles are used to define invariants of knots and examples of calculations for classical knots with up to $8$ crossings and classical links with up to $7$ crossings are provided.

Citation

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Mohamed Elhamdadi. Sam Nelson. "$N$-degeneracy in rack homology and link invariants." Hiroshima Math. J. 42 (1) 127 - 142, March 2012. https://doi.org/10.32917/hmj/1333113010

Information

Published: March 2012
First available in Project Euclid: 30 March 2012

zbMATH: 1310.57022
MathSciNet: MR2952076
Digital Object Identifier: 10.32917/hmj/1333113010

Subjects:
Primary: 57M25, 57M27

Rights: Copyright © 2012 Hiroshima University, Mathematics Program

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Vol.42 • No. 1 • March 2012
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