Annihilation of torsion in homology of finite m-AQ quandles

2015/10/12 by Józef H. Przytycki, Przytycki, Józef H., Seung Yeop Yang +1 · 1 citation
Mathematics · #18G60 #55N35 #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:18G60 #msc:55N35 #msc:57M25

paper · pdf · doi:10.48550/arxiv.1510.03464

13 pages, 2 figures

arxiv created 2015/10/12 · arxiv updated 2015/10/14

Abstract

It is a classical result in reduced homology of finite groups that the order of a group annihilates its homology. Similarly, we have proved that the torsion subgroup of rack and quandle homology of a finite quasigroup quandle is annihilated by its order. However, it does not hold for connected quandles in general. In this paper, we define an m-almost quasigroup (m-AQ) quandle which is a generalization of a quasigroup quandle and study annihilation of torsion in its rack and quandle homology groups.

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