Explicit horizontal open books on some plumbings

Details Explicit horizontal open books on some plumbings Explicit horizontal open books on some plumbings

2005-09-26

arxiv.org/abs/math/0509611v2

Internat. J. Math. 17 (2006), 1013-1031

Mathematics

Geometric Topology

20 pages, 15 figures

Scientific paper

We describe explicit open books on arbitrary plumbings of oriented circle bundles over closed oriented surfaces. We show that, for a non-positive plumbing, the open book we construct is horizontal and the corresponding compatible contact structure is also horizontal and Stein fillable. In particular, we describe horizontal open books on some Seifert fibered 3--manifolds. As another application we describe horizontal open books isomorphic to Milnor open books for some complex surface singularities. Moreover we give examples of tight contact 3--manifolds supported by planar open books. As a consequence the Weinstein conjecture holds for these tight contact structures.

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