On the topology of broken Lefschetz fibrations and near-symplectic four-manifolds
On the topology of broken Lefschetz fibrations and near-symplectic four-manifolds
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破碎 Lefschetz 纤维和近辛四流形的拓扑
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发表时间：
2007
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通讯作者：
R. Baykur
中科院分区：
文献类型：
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作者：
R. Baykur
利用手柄分解的方法研究了破碎的Lefschetz原纤维的拓扑结构。我们考虑对圆形句柄稍加概括，并描述出现在第四维中的所有句柄图。我们建立了破碎的Lefschetz纤维/铅笔的某个子类的简化手体和单轴表示，同时证明了所有近辛的闭4-流形都可以由这些表示支撑。给出了破碎Lefschetz原函数的各种构造，并将辛纤维和运算推广到近辛环境。扩展了对Lefschetz纤颤的研究，我们发现了辛纤维和运算的某些约束条件，从而得到具有非平凡Seiberg-Witten不变量的4-流形，以及破碎的Lefschetz纤颤的截面可以获得的自交数。
The topology of broken Lefschetz fibrations is studied by means of handle decompositions. We consider a slight generalization of round handles, and describe the handle diagrams for all that appear in dimension four. We establish simplified handlebody and monodromy representations for a certain subclass of broken Lefschetz fibrations/pencils, while showing that all near-symplectic closed 4-manifolds can be supported by these a la Auroux, Donaldson, Katzarkov. Various constructions of broken Lefschetz fibrations and a generalization of the symplectic fiber sum operation to the near-symplectic setting are given. Extending the study of Lefschetz fibrations, we detect certain constraints on the symplectic fiber sum operation to result in a 4-manifold with nontrivial Seiberg-Witten invariant, as well as the self-intersection numbers that sections of broken Lefschetz fibrations can acquire.