A note on Chern-Weil classes of Cartan connections

Key Points

• To construct Chern–Weil characteristic classes for Cartan connections relative to a model Cartan geometry.
• Defined a subalgebra of polynomials on the Atiyah algebroid for a fixed Cartan geometry.
• Established a characteristic map for Cartan geometries sharing the same underlying group representation.
• Analyzed the relationship between the characteristic map and de Rham cohomology of the base manifold.
• The characteristic map retrieves the classical Chern–Weil map for Cartan connections from Klein geometries.
• Demonstrated the existence of characteristic classes related to different Cartan geometries.

Abstract