Algebraic and Geometric Topology 3 (2003),
paper no. 19, pages 569-586.
Open books and configurations of symplectic surfaces
David T. Gay
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.
Symplectic, contact, concave, open book, plumbing, fillable
AMS subject classification.
Secondary: 57N10, 57N13.
Note: There is an erratum to this paper which should
be read alongside it.
Submitted: 27 January 2003.
Accepted: 23 April 2003.
Published: 20 June 2003.
Notes on file formats
David T. Gay
Department of Mathematics, University of Arizona
617 North Santa Rita, PO Box 210089
Tucson, AZ 85721, USA
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