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A Chern-Weil theory for Lie groupoids with Cartan connections
Abstract
We extend Chern-Weil theory to Lie groupoids carrying a Cartan connection. For a principal $(Σ, ω)$-bundle $(P, θ)$ over X we construct a map of differential graded algebras from an ω-basic subcomplex of the Weil algebra of the Lie algebroid of Σ to Ω•(X), whose map in cohomology does not depend on θ. It recovers the classical Chern-Weil map for Lie groups, the Cartan model for action groupoids, and the characteristic classes of Cartan geometries for gauge groupoids.
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BibTeX
@misc{accornero2026chernweil,
title = {{A Chern-Weil theory for Lie groupoids with Cartan connections}},
author = {Luca Accornero and Mateus de Melo and Ivan Struchiner},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31219},
eprint = {2610.31219},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31219},
}
RIS
TY - UNPB
TI - A Chern-Weil theory for Lie groupoids with Cartan connections
AU - Luca Accornero
AU - Mateus de Melo
AU - Ivan Struchiner
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31219
UR - https://arxiv.org/abs/2610.31219
AB - We extend Chern-Weil theory to Lie groupoids carrying a Cartan connection. For a principal $(Σ, ω)$-bundle $(P, θ)$ over X we construct a map of differential graded algebras from an ω-basic subcomplex of the Weil algebra of the Lie algebroid of Σ to Ω^•(X), whose map in cohomology does not depend on θ. It recovers the classical Chern-Weil map for Lie groups, the Cartan model for action groupoids, and the characteristic classes of Cartan geometries for gauge groupoids.
ER -