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Invariance of immersed Floer cohomology under Maslov flows

Joseph Palmer and Chris Woodward

Algebraic & Geometric Topology 21 (2021) 2313–2410
Abstract

We show that immersed Lagrangian Floer cohomology in compact rational symplectic manifolds is invariant under Maslov flow; this includes coupled mean curvature/Kähler–Ricci flow in the sense of Smoczyk (Leipzig University, 2001). In particular, we show invariance when a pair of self-intersection points is born or dies at a self-tangency, using results of Ekholm, Etnyre and Sullivan (J. Differential Geom. 71 (2005) 177–305). Using this we prove a lower bound on the time for which the immersed Floer theory is invariant under the flow, if it exists. This proves part of a conjecture of Joyce (EMS Surv. Math. Sci. 2 (2015) 1–62).

Keywords
Floer cohomology, mean curvature flow, weakly bounding cochains
Mathematical Subject Classification 2010
Primary: 53D40
References
Publication
Received: 13 August 2019
Revised: 22 October 2020
Accepted: 15 December 2020
Published: 31 October 2021
Authors
Joseph Palmer
Department of Mathematics
University of Illinois at Urbana Champaign
Urbana, IL
United States
Chris Woodward
Department of Mathematics
Rutgers University
Piscataway, NJ
United States