Introduction to the Tangent Grupoid

TL;DR

This paper introduces the concept of the tangent grupoid of a manifold, providing plausible definitions and discussing known applications, serving as an introductory overview of this mathematical structure.

Contribution

It offers initial definitions and applications of the tangent grupoid, contributing to the foundational understanding of this mathematical concept.

Findings

Proposed plausible definitions for the tangent grupoid.

Discussed applications of the tangent grupoid in geometry.

Served as an introductory note to the topic.

Abstract

We present some plausible definitions for the tangent grupoid of a manifold M, as well as some of the known applications of the structure. This is a kind of introductory note.