# Deformation of singular foliations, 1: Local deformation cohomology

## TL;DR

This paper introduces a new cohomology framework to study local deformations of singular foliations, integrable forms, and Nambu structures, providing tools to analyze their infinitesimal changes near a point.

## Contribution

It defines deformation cohomology for singular foliations and related structures, focusing on local behavior, which is a novel approach in the field.

## Key findings

- Established the concept of local deformation cohomology for singular foliations.
- Analyzed the properties of this cohomology in the neighborhood of a point.
- Provided foundational results for future deformation studies of singular geometric structures.

## Abstract

In this paper we introduce the notion of deformation cohomology for singular foliations and related objects (namely integrable differential forms and Nambu structures), and study it in the local case, i.e., in the neighborhood of a point.