Subflexible symplectic manifolds

Murphy, Emmy; Siegel, Kyler

doi:10.2140/gt.2018.22.2367

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Subflexible symplectic manifolds

Emmy Murphy and Kyler Siegel

Geometry & Topology 22 (2018) 2367–2401

DOI: 10.2140/gt.2018.22.2367

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.

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

Volume 22, issue 4 (2018)