N-Degeneracy in rack homology and link invariants

Details N-Degeneracy in rack homology and link invariants N-Degeneracy in rack homology and link invariants

2010-07-21

arxiv.org/abs/1007.3550v2

Mathematics

Geometric Topology

12 pages; revisions as requested by referee

Scientific paper

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.

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