Invariance of immersed Floer cohomology under Maslov flows

Palmer, Joseph; Woodward, Chris

doi:10.2140/agt.2021.21.2313

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Invariance of immersed Floer cohomology under Maslov flows

Joseph Palmer and Chris Woodward

Algebraic & Geometric Topology 21 (2021) 2313–2410

DOI: 10.2140/agt.2021.21.2313

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

Volume 21, issue 5 (2021)