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arXiv · 1804.06799

Invariance of Immersed Floer cohomology under Maslov flows

Joseph Palmer·Chris Woodward·with an erratum written jointly with Hadi Azizi
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Abstract

We show that immersed Lagrangian Floer cohomology in compact rational symplectic manifolds is invariant under Maslov flows such as coupled mean curvature/Kaehler-Ricci flow in the sense of Smoczyk as a pair of self-intersection points is born or dies at a self-tangency, using results of Ekholm-Etnyre-Sullivan. This proves part of a conjecture of Joyce. We give a lower bound on the time for which the Floer cohomology is invariant under the (forward or backwards) flow, if it exists. This post-publication has an erratum written jointly with Hadi Azizi, which fills in a missing case in the proof Lemma 7.9 (b).

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Joseph Palmer, Chris Woodward, with an erratum written jointly with Hadi Azizi. 2018-04-18. Invariance of Immersed Floer cohomology under Maslov flows. https://doi.org/10.2140/agt.2021.21.2313

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