Homotopy theory of singular foliations

Abstract

In this article we apply ideas from homotopy theory to the study of singular foliations. We verify that a technical lemma remains valid for left semi-model categories. When applied to the category of $L_{\infty }$-algebroids thanks to the work of Nuiten, this lemma enables to recover results very similar to those of Laurent-Gengoux and al. about existence and (up to homotopy) uniqueness of universal $L_{\infty }$-algebroids associated to a singular foliation. We conclude with some open questions.

comments are welcome

Cited by in corpus (1)

• Lie-Rinehart algebra $\simeq$ acyclic Lie $\infty$-algebroid