Commuting foliations

TL;DR

This paper extends the concept of commuting vector fields to singular foliations through Nambu structures, classifying their relationships and establishing foundational results about their commutativity.

Contribution

It introduces a novel framework connecting singular foliations with Nambu structures and explores their commutativity properties.

Findings

Classification of relationships between singular foliations and Nambu structures

Basic results on commuting Nambu structures

Extension of vector field commutativity to singular foliations

Abstract

The aim of this paper is to extend the notion of commutativity of vector fields to the category of singular foliations, using Nambu structures, i.e. integrable multi-vector fields. We will classify the relationship between singular foliations and Nambu structures, and show some basic results about commuting Nambu structures.