Involutive bordered Floer homology

Hendricks, Kristen; Lipshitz, Robert

doi:10.1090/tran/7557

Involutive bordered Floer homology
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by Kristen Hendricks and Robert Lipshitz PDF

Trans. Amer. Math. Soc. 372 (2019), 389-424

Abstract:

We give a bordered extension of involutive $\widehat {HF}$ and use it to give an algorithm to compute involutive $\widehat {HF}$ for general $3$-manifolds. We also explain how the mapping class group action on $\widehat {HF}$ can be computed using bordered Floer homology. As applications, we prove that involutive $\widehat {HF}$ satisfies a surgery exact triangle and compute $\widehat {HFI}(\Sigma (K))$ for all 10-crossing knots $K$.

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