Topological equivalence of holomorphic foliation germs of rank $1$ with isolated singularity in the Poincaré domain

Thomas Eckl; Michael Lönne

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arXiv · 1601.00090

Topological equivalence of holomorphic foliation germs of rank $1$ with isolated singularity in the Poincaré domain

Thomas Eckl·Michael Lönne

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Abstract

We show that the topological equivalence class of holomorphic foliation germs with an isolated singularity of Poincaré type is determined by the topological equivalence class of the real intersection foliation of the (suitably normalized) foliation germ with a sphere centered in the singularity. We use this Reconstruction Theorem to completely classify topological equivalence classes of plane holomorphic foliation germs of Poincaré type and discuss a conjecture on the classification in dimension $\geq 3$.

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Thomas Eckl, Michael Lönne. 2017-07-19. Topological equivalence of holomorphic foliation germs of rank $1$ with isolated singularity in the Poincaré domain. https://arxiv.org/abs/1601.00090

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