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Subflexible symplectic manifolds

Emmy Murphy and Kyler Siegel

Geometry & Topology 22 (2018) 2367–2401
Abstract

We introduce a class of Weinstein domains which are sublevel sets of flexible Weinstein manifolds but are not themselves flexible. These manifolds exhibit rather subtle behavior with respect to both holomorphic curve invariants and symplectic flexibility. We construct a large class of examples and prove that every flexible Weinstein manifold can be Weinstein homotoped to have a nonflexible sublevel set.

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Keywords
symplectic geometry, Weinstein manifolds, h principles, symplectic cohomology, polynomial convexity, exotic symplectic structures
Mathematical Subject Classification 2010
Primary: 53D35
Secondary: 32E20
References
Publication
Received: 8 December 2016
Revised: 16 July 2017
Accepted: 17 August 2017
Published: 5 April 2018
Proposed: Leonid Polterovich
Seconded: Ciprian Manolescu, András I Stipsicz
Authors
Emmy Murphy
Department of Mathematics
Massachusetts Institute of Technology
Cambridge
MA
United States
Kyler Siegel
Department of Mathematics
Massachusetts Institute of Technology
Cambridge
MA
United States