Cartan geometries and multiplicative forms

TL;DR

This paper introduces a new perspective on Cartan geometries using transitive Lie groupoids with multiplicative forms, leading to the broader concept of Cartan bundles that unify geometrical structures.

Contribution

It presents a novel approach to studying Cartan geometries through Lie groupoids and defines Cartan bundles as a generalization of existing structures.

Findings

Cartan geometries can be analyzed via transitive Lie groupoids with multiplicative forms.

The concept of Cartan bundle generalizes Cartan geometries and G-structures.

Provides a unified framework for different geometric structures.

Abstract

In this paper we show that Cartan geometries can be studied via transitive Lie groupoids endowed with a special kind of vector-valued multiplicative 1-forms. This viewpoint leads us to a more general notion, that of Cartan bundle, which encompasses both Cartan geometries and G-structures.