Non-abelian tensor product and circular orderability of groups

Abstract

For a group G we consider its tensor square $G\otimes G$ and exterior square $G\wedge G$. We prove that for a circularly orderable group G, under some assumptions on $H_1\left(G\right)$ and $H_2\left(G\right)$, its exterior square and tensor square are left-orderable. This yields an obstruction for a circularly orderable group G to have torsion. We apply these results to study circular orderability of tabulated virtual knot groups.