Atiyah sequences and connections on principal bundles over differentiable stacks

TL;DR

This paper develops a framework for understanding connections on principal bundles over differentiable stacks and Lie groupoids using Atiyah sequences, advancing the mathematical tools for studying geometric structures on stacks.

Contribution

It introduces a novel approach to define and analyze connections on principal bundles over stacks via Atiyah sequences and transversal distributions.

Findings

Established a new construction of connections on stacks.

Extended Atiyah sequences to differentiable stacks and Lie groupoids.

Provided foundational tools for future geometric and topological studies on stacks.

Abstract

We construct and study general connections on Lie groupoids and differentiable stacks as well as on principal bundles over them using Atiyah sequences associated to transversal tangential distributions.