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

Francesco Lin

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arXiv · 1809.01637

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

Francesco Lin

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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.

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Francesco Lin. 2018-09-05. Non-formality in $\mathrm{Pin}(2)$-monopole Floer homology. https://arxiv.org/abs/1809.01637

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