TY - JOUR
T1 - On quandle homology groups of Alexander quandles of prime order
AU - Nosaka, Takefumi
PY - 2013/7
Y1 - 2013/7
N2 - 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.
AB - 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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U2 - 10.1090/S0002-9947-2013-05754-6
DO - 10.1090/S0002-9947-2013-05754-6
M3 - Article
AN - SCOPUS:84876425725
VL - 365
SP - 3413
EP - 3436
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 7
ER -