Geometry & Topology

Subflexible symplectic manifolds

Emmy Murphy and Kyler Siegel

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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.

Article information

Geom. Topol., Volume 22, Number 4 (2018), 2367-2401.

Received: 8 December 2016
Revised: 16 July 2017
Accepted: 17 August 2017
First available in Project Euclid: 13 April 2018

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53D35: Global theory of symplectic and contact manifolds [See also 57Rxx]
Secondary: 32E20: Polynomial convexity

symplectic geometry Weinstein manifolds h principles symplectic cohomology polynomial convexity exotic symplectic structures


Murphy, Emmy; Siegel, Kyler. Subflexible symplectic manifolds. Geom. Topol. 22 (2018), no. 4, 2367--2401. doi:10.2140/gt.2018.22.2367.

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