Trisections of Lefschetz Pencils
Trisections of Lefschetz Pencils
复制标题
莱夫谢茨铅笔的三等分
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
David T. Gay
中科院分区：
文献类型：
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作者：
David T. Gay
访问数/每百万人：Reach for[J.53(1999)205-236]证明了每个闭辛4-流形都可以被赋予拓扑Lefschetz铅笔的结构。访问数/每百万人：Reach for[Geom.白杨。20(2016)3097-3132]证明了每个闭4-流形都有一个三等分。在这篇文章中，我们将这两个结构定理联系起来，展示了如何从一个拓扑Lefschetz铅笔直接构造一个三等分。这种三等分是这样的，即三个扇区中的每一个都是铅笔的规则纤维的规则邻域。这是以下平凡的3维结果的4维模拟：对于3-流形M的每一个开卷分解，都有一个M分解成3个手柄，每个手柄是页面的正则邻域。
Donaldson [J. Differential Geom. 53 (1999) 205–236] showed that every closed symplectic 4–manifold can be given the structure of a topological Lefschetz pencil. Gay and Kirby [Geom. Topol. 20 (2016) 3097–3132] showed that every closed 4–manifold has a trisection. In this paper we relate these two structure theorems, showing how to construct a trisection directly from a topological Lefschetz pencil. This trisection is such that each of the three sectors is a regular neighborhood of a regular fiber of the pencil. This is a 4–dimensional analog of the following trivial 3–dimensional result: for every open book decomposition of a 3–manifold M , there is a decomposition of M into three handlebodies, each of which is a regular neighborhood of a page.