1. ON QUANDLE HOMOLOGY GROUPS OF ALEXANDER QUANDLES OF PRIME ORDER.
- Author
-
NOSAKA, TAKEFUMI
- Subjects
HOMOLOGY theory ,GROUP theory ,COCYCLES ,TOPOLOGICAL degree ,PRIME numbers ,FIBONACCI sequence ,COHOMOLOGY theory - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2013
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