Algebraic & Geometric Topology

Open books and configurations of symplectic surfaces

David T Gay

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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.

Article information

Algebr. Geom. Topol., Volume 3, Number 1 (2003), 569-586.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R17: Symplectic and contact topology
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx] 57N13: Topology of $E^4$ , $4$-manifolds [See also 14Jxx, 32Jxx]

symplectic contact concave open book plumbing fillable


Gay, David T. Open books and configurations of symplectic surfaces. Algebr. Geom. Topol. 3 (2003), no. 1, 569--586. doi:10.2140/agt.2003.3.569.

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