Topological complexity of symplectic 4-manifolds and Stein fillings
Topological complexity of symplectic 4-manifolds and Stein fillings
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DOI：
10.4310/jsg.2016.v14.n1.a7
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发表时间：
2012-12
期刊：
影响因子：
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通讯作者：
R. Baykur;Jeremy Van Horn-Morris
中科院分区：
文献类型：
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作者：
R. Baykur;Jeremy Van Horn-Morris
证明了仅来自相容Lefschetz铅笔亏格的闭辛4-流形的Euler特征线不存在先验界，也不存在来自相容开书亏格的切触3-流形的Stein填充的先验界-可能除了少数低亏格的情形.为了得到我们的结果，我们产生的第一个例子的因式分解的边界平行德恩扭曲任意长的产品的正德恩扭曲沿着非分离曲线上的一个固定的表面与边界。这解决了Auroux，Smith和Wajnryb提出的一个开放问题，以及Korkmaz，Ozbagci和Stipsicz独立提出的一个更一般的变体。
We prove that there exists no a priori bound on the Euler characteristic of a closed symplectic 4-manifold coming solely from the genus of a compatible Lefschetz pencil on it, nor is there a similar bound for Stein fillings of a contact 3-manifold coming from the genus of a compatible open book --- except possibly for a few low genera cases. To obtain our results, we produce the first examples of factorizations of a boundary parallel Dehn twist as arbitrarily long products of positive Dehn twists along non-separating curves on a fixed surface with boundary. This solves an open problem posed by Auroux, Smith and Wajnryb, and a more general variant of it raised by Korkmaz, Ozbagci and Stipsicz, independently.