Atiyah sequences, connections and Chern-Weil theory for algebraic and differentiable stacks

TL;DR

This paper develops a framework for constructing connections and characteristic forms on principal bundles over stacks and groupoids across various categories, utilizing Atiyah sequences linked to transversal distributions.

Contribution

It introduces a novel method to define connections and characteristic forms for bundles over stacks using Atiyah sequences, bridging differential, algebraic, and holomorphic contexts.

Findings

Established a construction of connections on principal bundles over stacks.

Extended Chern-Weil theory to algebraic and differentiable stacks.

Unified approach across multiple categories for bundle characteristic classes.

Abstract

We construct connections and characteristic forms for principal bundles over groupoids and stacks in the differentiable, holomorphic and algebraic category using Atiyah sequences associated to transversal tangential distributions.