四维流形I的拉格朗日匹配不变量
Lagrangian matching invariants for fibred four-manifolds: I
摘要：
在一对文件中，我们构造不变量光滑的四个流形配备了“破纤维”-奇异的莱夫谢茨纤维的Auroux，唐纳森和Katzarkov -推广的唐纳森史密斯不变量莱夫谢茨纤维。“拉格朗日匹配不变量”被设计成与基础四流形的Seiberg-Witten不变量相比较。他们适合到分配弗洛尔同调群的域论的三维流形。的不变量来自模空间的伪全纯部分的相对希尔伯特计划的纤维上的点，拉格朗日边界条件。第一部分是专门的辛几何这些拉格朗日。
英文摘要：
In a pair of papers, we construct invariants for smooth four-manifolds equipped with `broken fibrations' - the singular Lefschetz fibrations of Auroux, Donaldson and Katzarkov - generalising the Donaldson-Smith invariants for Lefschetz fibrations. The `Lagrangian matching invariants' are designed to be comparable with the Seiberg-Witten invariants of the underlying four-manifold. They fit into a field theory which assigns Floer homology groups to fibred 3-manifolds. The invariants are derived from moduli spaces of pseudo-holomorphic sections of relative Hilbert schemes of points on the fibres, subject to Lagrangian boundary conditions. Part I is devoted to the symplectic geometry of these Lagrangians.
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