A note on Chern-Weil classes of Cartan connections

2025/05/01 by Accornero, Luca, de Melo, Mateus M., Struchiner, Ivan
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.00247

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,ω) with underlying data (G,V) and a second Cartan geometry (P,θ) 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,ω) arises from a Klein pair modeling (P,θ).

Citations

• Pfaffian groupoids
• Multiplicative Forms and Spencer Operators
• Geometric structures as deformed infinitesimal symmetries
• Differential geometry of Cartan connections

Related

• Connections on Lie groupoids and Chern-Weil theory
• Connections up to homotopy and characteristic classes
• Chern characters via connections up to homotopy
• Morphisms of Cartan connections
• Characteristic forms of complex Cartan geometries III: G-structures