On singular foliations tangent to a given hypersurface

Michael Francis

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arXiv · 2311.03940

On singular foliations tangent to a given hypersurface

Michael Francis

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Abstract

We consider a class of singular foliations in the sense of Androulidakis and Skandalis that we call transverse order $k$ foliations. These have a finite number of leaves: one hypersurface (the singular leaf) together with the components of its complement (open leaves). The positive integer parameter $k$ encodes the "order of tangency" of the leafwise vector fields to $L$. We show that a loop in the singular leaf induces a well-defined holonomy transformation at the level of $(k-1)$-jets. The resulting holonomy invariant can be used to give a complete classification of these foliations and obtain concrete descriptions of their associated groupoids and algebras.

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Michael Francis. 2023-11-07. On singular foliations tangent to a given hypersurface. https://arxiv.org/abs/2311.03940

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