Subflexible symplectic manifolds

Emmy Murphy; Kyler Siegel

doi:10.2140/gt.2018.22.2367

Subflexible symplectic manifolds

Emmy Murphy, Kyler Siegel

Research output: Contribution to journal › Article › peer-review

14 Scopus citations

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.

Original language	English (US)
Pages (from-to)	2367-2401
Number of pages	35
Journal	Geometry and Topology
Volume	22
Issue number	4
DOIs	https://doi.org/10.2140/gt.2018.22.2367
State	Published - Apr 5 2018
Externally published	Yes

All Science Journal Classification (ASJC) codes

Geometry and Topology

Keywords

Exotic symplectic structures
H principles
Polynomial convexity
Symplectic cohomology
Symplectic geometry
Weinstein manifolds

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10.2140/gt.2018.22.2367

Cite this

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title = "Subflexible symplectic manifolds",

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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AB - 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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KW - H principles

KW - Polynomial convexity

KW - Symplectic cohomology

KW - Symplectic geometry

KW - Weinstein manifolds

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JO - Geometry and Topology

JF - Geometry and Topology

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Subflexible symplectic manifolds

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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