Lefschetz fibrations on compact Stein surfaces

Details Lefschetz fibrations on compact Stein surfaces Lefschetz fibrations on compact Stein surfaces

2000-12-22

arxiv.org/abs/math/0012239v4

Mathematics

Geometric Topology

This is the corrected full-version of what has already appeared in GT. (Later GT may re-post its own corrected short-version)

Scientific paper

The existence of a positive allowable Lefschetz fibration on a compact Stein surface with boundary was established by Loi and Piergallini by using branched covering techniques. Here we give an alternative simple proof of this fact and construct explicitly the vanishing cycles of the Lefschetz fibration, obtaining a direct identification of the set of compact Stein manifolds with positive allowable Lefschetz fibrations over a 2-disk. In the process we associate to every compact Stein manifold infinitely many nonequivalent such Lefschetz fibrations.

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