Geodesic
Open books and configurations of symplectic surfaces
Gay, David T1
1Department of Mathematics, University of Arizona, 617 North Santa Rita, PO Box 210089, Tucson, AZ 85721, USA
Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 569-586
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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.

DOI : 10.2140/agt.2003.3.569
Keywords: symplectic, contact, concave, open book, plumbing, fillable

Gay, David T  1

1 Department of Mathematics, University of Arizona, 617 North Santa Rita, PO Box 210089, Tucson, AZ 85721, USA 
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Gay, David T. Open books and configurations of symplectic surfaces. Algebraic and Geometric Topology, Tome 3 (2003) no. 1, pp. 569-586. doi: 10.2140/agt.2003.3.569

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