The equivariant Chern character for non-compact Lie groups (Q1342378)

If \(G\) is a Lie group, \(EG\) its classifying bundle, and \(M\) is a differentiable manifold with a smooth left \(G\)-action, then the equivariant cohomology \(H^*_G (M)\) of \(M\) is the cohomology of a homotopy quotient \(M_G= EG\times_G M\). The author presents a new model for \(H^*_G (M)\) and obtains an explicit formula for the equivariant Chern class similar to the Chern-Weil formula for the ordinary Chern class. His Chern character specializes to that of Bott if \(G\) is discrete, and to that of Berline and Vergne if \(G\) is compact and the connection of the equivariant bundle is \(G\)-invariant.