Abstract We give the construction of the universal, natural up to homotopy Chern–Weil differential graded algebra homomorphism: for infinite‐dimensional Milnor regular Lie groups , where is a certain de Rham algebra of (Milnor up to a natural weak homotopy equivalence) and where is the algebra of continuous invariant multilinear functionals on the Lie algebra. In particular, this applies to the group of compactly generated Hamiltonian symplectomorphisms, using which we verify a conjecture of Reznikov. For the construction of , we introduce a basic geometric‐categorical notion of a smooth simplicial set. Loosely, this is to Chen spaces as simplicial sets are to spaces. We then give a new construction of the classifying space of as a smooth Kan complex, with the geometric realization weakly equivalent to the Milnor .
Yasha Savelyev (Thu,) studied this question.