Atiyah sequences and connections on principal bundles over differentiable stacks
Indranil Biswas, Saikat Chatterjee, Praphulla Koushik, and Frank, Neumann

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.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Advanced Topics in Algebra
