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.

中文翻译：

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PIN（2）-单极Floer同源性中的非形式性

在先前的工作中，我们在封闭的，定向的三歧管$ Y $的Pin（2）-单极Floer链复合体上引入了自然的$ \ mathcal {A} _ {\ infty} $结构，并证明它是在最简单的情况下是非正规的，其中$ Y $是三个球体$ S ^ 3 $。在本文中，我们将进一步探讨这种非形式现象。具体来说，我们提供了几种由同源性引起的梅西乘积的显式描述，并讨论了在连接和的Pin（2）-单极Floer同源性计算中的应用。