Topology Seminar

Speaker:        Seung Yeop Yang (GWU)
Title:          Torsion in rack homology

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 (see Journal of Pure and Applied Algebra, 2015). But it does not hold for connected quandles in general. In this paper, we define an m-almost quasigroup quandle which is a generalization of a quasigroup quandle and study annihilation of its rack and quandle homology groups. We then construct some families of connected quandles for which torsion subgroups of rack and quandle homology are annihilated by the orders of their quandle inner automorphism groups.