We present a construction of Chern–Weil characteristic classes for Cartan connections relative to a “model” Cartan geometry. More precisely, given a fixed Cartan geometry we define a subalgebra of polynomials on its Atiyah algebroid such that any other Cartan geometry with the same underlying group representation comes with a characteristic map defined on such subalgebra and taking values in the de Rham cohomology of the base manifold. The characteristic map recovers the classical Chern–Weil map of a Cartan connection when the “model” Cartan geometry arises from a Klein geometry.
Accornero et al. (Fri,) studied this question.
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