The Linearizability of Singular Foliations Is a Morita Invariant

Abstract

Hausdorff Morita equivalence is an equivalence relation on singular foliations, which induces a bijection between their leaves. Our main statement is that linearizability along a leaf is invariant under Hausdorff Morita equivalence. The proof relies on a characterization of tubular neighborhood embeddings using Euler-like vector fields.