Lefschetz fibrations on compact Stein surfaces
几何拓扑
2014-11-26 v4 代数几何
摘要
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.
引用
@article{arxiv.math/0012239,
title = {Lefschetz fibrations on compact Stein surfaces},
author = {Selman Akbulut and Burak Ozbagci},
journal= {arXiv preprint arXiv:math/0012239},
year = {2014}
}
备注
This is the corrected full-version of what has already appeared in GT. (Later GT may re-post its own corrected short-version)