On quandle homology groups of Alexander quandles of prime order

Author:
Takefumi Nosaka

Journal:
Trans. Amer. Math. Soc. **365** (2013), 3413-3436

MSC (2010):
Primary 20G10, 55N35, 58H10; Secondary 57Q45, 57M25, 55S20

Published electronically:
January 30, 2013

MathSciNet review:
3042590

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Abstract: In this paper we determine the integral quandle homology groups of Alexander quandles of prime order. As a special case, this settles the *delayed Fibonacci conjecture* by M. Niebrzydowski and J. H. Przytycki from their 2009 paper. Further, we determine the cohomology group of the Alexander quandle and obtain relatively simple presentations of all higher degree cocycles which generate the cohomology group. Finally, we prove that the integral quandle homology of a finite connected Alexander quandle is annihilated by the order of the quandle.

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Additional Information

**Takefumi Nosaka**

Affiliation:
Research Institute for Mathematical Sciences, Kyoto University, Sakyo-ku, Kyoto, 606-8502, Japan

Email:
nosaka@kurims.kyoto-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-2013-05754-6

Keywords:
Rack,
quandle,
homology,
cohomology,
knot

Received by editor(s):
November 17, 2009

Received by editor(s) in revised form:
April 1, 2011

Published electronically:
January 30, 2013

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.