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2003 Open books and configurations of symplectic surfaces
David T Gay
Algebr. Geom. Topol. 3(1): 569-586 (2003). DOI: 10.2140/agt.2003.3.569

Abstract

We study neighborhoods of configurations of symplectic surfaces in symplectic 4–manifolds. We show that suitably “positive” configurations have neighborhoods with concave boundaries and we explicitly describe open book decompositions of the boundaries supporting the associated negative contact structures. This is used to prove symplectic nonfillability for certain contact 3–manifolds and thus nonpositivity for certain mapping classes on surfaces with boundary. Similarly, we show that certain pairs of contact 3–manifolds cannot appear as the disconnected convex boundary of any connected symplectic 4–manifold. Our result also has the potential to produce obstructions to embedding specific symplectic configurations in closed symplectic 4–manifolds and to generate new symplectic surgeries. From a purely topological perspective, the techniques in this paper show how to construct a natural open book decomposition on the boundary of any plumbed 4–manifold.

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David T Gay. "Open books and configurations of symplectic surfaces." Algebr. Geom. Topol. 3 (1) 569 - 586, 2003. https://doi.org/10.2140/agt.2003.3.569

Information

Received: 27 January 2003; Accepted: 23 October 2002; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1035.57015
MathSciNet: MR1997330
Digital Object Identifier: 10.2140/agt.2003.3.569

Subjects:
Primary: 57R17
Secondary: 57N10, 57N13

Rights: Copyright © 2003 Mathematical Sciences Publishers

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