Topological equivalence of holomorphic foliation germs of rank 1 with isolated singularity in the Poincar/'e domain

Eckl, T and Loenne, Michael (2019) Topological equivalence of holomorphic foliation germs of rank 1 with isolated singularity in the Poincar/'e domain. Annales de l'Institut Fourier, 69 (2). pp. 561-590.

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Abstract

We show that the topological equivalence class of holomorphic foliation germs of rank 1 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 ≥3.

Item Type:	Article
Uncontrolled Keywords:	holomorphic foliation germs, isolated singularity, topological equivalence, Poincaré domain
Depositing User:	Symplectic Admin
Date Deposited:	09 May 2019 11:47
Last Modified:	19 Jan 2023 00:53
DOI:	10.5802/aif.3251
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3038208

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• Topological equivalence of holomorphic foliation germs of rank 1 with isolated singularity in the Poincar/'e domain'. (deposited 09 Jul 2018 06:09)
  • Topological equivalence of holomorphic foliation germs of rank 1 with isolated singularity in the Poincar/'e domain. (deposited 09 May 2019 11:47) [Currently Displayed]