Constructing Lefschetz-type fibrations on four-manifolds
Constructing Lefschetz-type fibrations on four-manifolds
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在四流形上构造 Lefschetz 型纤维
DOI：
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发表时间：
2007
期刊：
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通讯作者：
R. Kirby
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文献类型：
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作者：
David T. Gay;R. Kirby
我们展示了如何在任意光滑的、闭的、定向的4-流形上构造断裂的、非手性的Lefschetz纤维化。这些是2-球面上Lefschetz纤维化的推广，其中我们允许具有非标准方向的Lefschetz奇点以及对应于圆形1-手柄的奇点圆。我们也可以安排一个给定的面积为0的正方形是一个纤维。在没有3-和4-句柄的4-流形的二重流形的情况下，构造更容易和更明确，例如由平凡群的非平凡平衡表示产生的同伦4-球面。57 M50; 57 R17
We show how to construct broken, achiral Lefschetz fibrations on arbitrary smooth, closed, oriented 4‐manifolds. These are generalizations of Lefschetz fibrations over the 2‐sphere, where we allow Lefschetz singularities with the non-standard orientation as well as circles of singularities corresponding to round 1‐handles. We can also arrange that a given surface of square 0 is a fiber. The construction is easier and more explicit in the case of doubles of 4‐manifolds without 3‐ and 4‐handles, such as the homotopy 4‐spheres arising from nontrivial balanced presentations of the trivial group. 57M50; 57R17