On quandle homology groups of Alexander quandles of prime order

Takefumi Nosaka

Research output: Contribution to journalArticlepeer-review

14 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)3413-3436
Number of pages24
JournalTransactions of the American Mathematical Society
Volume365
Issue number7
DOIs
Publication statusPublished - Jul 2013

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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