Non-formality in PIN(2)-monopole Floer homology

Abstract

In previous work, we introduced a natural $\mathcal{A}\_{\infty}$-structure on the Pin(2)-monopole Floer chain complex of a closed, oriented three-manifold $Y$, and showed that it is non-formal in the simplest case in which $Y$ is the three-sphere $S^3$. In this paper, we explore further this non-formality phenomenon. Specifically, we provide explicit descriptions of several Massey products induced on homology, and discuss applications to the computation of the Pin(2)-monopole Floer homology of connected sums.