N-Degeneracy in rack homology and link invariants
Geometric Topology
2011-05-24 v2 Quantum Algebra
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 [15]. 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 [6]. 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.
Cite
@article{arxiv.1007.3550,
title = {N-Degeneracy in rack homology and link invariants},
author = {Mohamed Elhamdadi and Sam Nelson},
journal= {arXiv preprint arXiv:1007.3550},
year = {2011}
}
Comments
12 pages; revisions as requested by referee