Lefschetz Fibrations on Compact Stein Manifolds

Details Lefschetz Fibrations on Compact Stein Manifolds Lefschetz Fibrations on Compact Stein Manifolds

2010-03-10

arxiv.org/abs/1003.2200v3

Mathematics

Geometric Topology

19 pages, and 6 figures

Scientific paper

Here we prove that a compact Stein manifold W of dimension 2n+2>4 admits a Lefschetz fibration over the 2-disk with Stein fibers, such that the monodromy of the fibration is a symplectomorphism induced by compositions of "generalized Dehn twists" along imbedded n-spheres on the generic fiber. Also, the open book on the boundary of W, which is determined by the fibration, is compatible with the contact structure induced by the Stein structure. This generalizes the Stein surface case of n=1, previously proven by Loi-Piergallini and Akbulut-Ozbagci.

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