The Linearizability of Singular Foliations Is a Morita Invariant

TL;DR

This paper proves that the property of linearizability along a leaf in singular foliations remains invariant under Hausdorff Morita equivalence, using tubular neighborhood embeddings characterized by Euler-like vector fields.

Contribution

It establishes that linearizability is a Morita invariant for singular foliations, providing a new perspective on their classification and invariance properties.

Findings

Linearizability along a leaf is invariant under Hausdorff Morita equivalence.

A characterization of tubular neighborhood embeddings using Euler-like vector fields.

The result links geometric properties of foliations with Morita equivalence.

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.