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arXiv · 2505.00247

A note on Chern-Weil classes of Cartan connections

Luca Accornero·Mateus M. de Melo·Ivan Struchiner
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Abstract

We present a construction of Chern-Weil characteristic classes for pairs Cartan geometries sharing the same underlying data. Given any model Cartan geometry $(Q,\omega)$ with underlying data $(G,V)$ and a second Cartan geometry $(P,\theta)$ with the same underlying data, we define a subalgebra of polynomials on the Atiyah algebroid of $Q$ together with a characteristic map that recovers the classical Chern-Weil map of a Cartan connection when $(Q,\omega)$ arises from a Klein pair modeling $(P,\theta)$.

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Luca Accornero, Mateus M. de Melo, Ivan Struchiner. 2025-05-01. A note on Chern-Weil classes of Cartan connections. https://doi.org/10.1016/j.difgeo.2026.102365

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