Non-formality in $\mathrm{Pin}(2)$-monopole Floer homology

Abstract

In previous work, we introduced a natural ${\mathcal{A}}_{\infty }$-structure on the $\mathrm{Pin}(2)$-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 provide explicit descriptions of several Massey products induced on homology, and discuss how they can be used to compute the $\mathrm{Pin}(2)$-monopole Floer homology of connected sums in many concrete examples.

41 pages, 2 figures. Comments are very welcome!

References in corpus (4)

• Algebra+Homotopy=Operad
• The symplectic arc algebra is formal
• Lectures on monopole Floer homology
• Manolescu correction terms and knots in the three-sphere