几何单值性与双曲圆盘
Geometric monodromy and the hyperbolic disc
摘要：
辛四流形产生Lefschetz纤维化，它是由映射类群中自由群的单值表示决定的。通过分析单值性对光滑纤维的泛覆盖的作用，研究了Lefschetz纤维化的拓扑结构。我们给出了新的和简单的证明，Lefschetz纤维化所产生的铅笔（即例外部分）从来没有分裂为非平凡的纤维和，没有简单闭曲线可以不变的单值表示下的合痕。
英文摘要：
Symplectic four-manifolds give rise to Lefschetz fibrations, which are determined by monodromy representations of free groups in mapping class groups. We study the topology of Lefschetz fibrations by analysing the action of the monodromy on the universal cover of a smooth fibre. We give new and simple proofs that Lefschetz fibrations arising from pencils (i.e. with exceptional sections) never split as non-trivial fibre sums, and that no simple closed curve can be invariant to isotopy under the monodromy representation.
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