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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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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: http://dx.doi.org/10.1090/S0002-9947-2013-05754-6
PII: S 0002-9947(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.