A Remark on Pin(2)-Equivariant Floer Homology

Abstract

In this remark, we show how the monopole Frøyshov invariant, as well as the analogues of the Involutive Heegaard Floer correction terms $\underline{d},\overline{d}$, are related to the $Pin\left(2\right)$-equivariant Floer homology ${\mathit{SWFH}}_{\ast }^G$. We show that the only interesting correction terms of a $Pin\left(2\right)$-space are those coming from the subgroups $\mathbb{Z}/4$, $S^1$, and $Pin\left(2\right)$ itself.