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Monodromy and topological classification of germs of holomorphic foliations

机译:全同叶型细菌的单峰性和拓扑分类

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摘要

We give a complete topological classification of germs of holomorphic foliations in the plane under rather generic conditions. The key point is the introduction of a new topological invariant called monodromy representation. This monodromy contains all the relevant dynamical information, in particular the projective holonomy representations whose topological inv ariance was conjectured in the eighties by Cerveau and Sad and is proved here under mild hypotheses.
机译:在相当普通的条件下,我们给出了平面上全同叶微生物的完整拓扑分类。关键是引入了称为单峰表示的新拓扑不变式。该单峰包含所有相关的动力学信息,尤其是射影全称学表示法,其拓扑学变化是由塞维奥和萨德在八十年代推测的,并在温和的假设下得到了证明。

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