Invariance of Immersed Floer cohomology under Maslov flows

TL;DR

This paper proves that immersed Floer cohomology remains invariant under certain geometric flows, specifically Maslov flows, in compact rational symplectic manifolds, confirming part of Joyce's conjecture.

Contribution

It establishes invariance of immersed Floer cohomology under Maslov flows and provides bounds on the flow duration for which invariance holds.

Findings

Floer cohomology is invariant under Maslov flows in certain manifolds.

Provides a lower bound on the time Floer cohomology remains invariant.

Includes an erratum addressing a missing case in a key lemma.

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).