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  1. ; ; (, Proceedings of symposia in pure mathematics)
    Connes, A.; Consani, C.; Dundas, B.; Khalkhali, M.; Moscovici, H. (Ed.)
    We give a simplified version of a construction due to Denis Perrot that recovers the Todd class of the complexified tangent bundle of a smooth manifold from a JLO-type cyclic cocycle. The construction takes place within an algebraic framework, rather than the customary functional-analytic frame- work of the JLO theory. The series expansion for the exponential function is used in place of the heat kernel from the functional-analytic theory; the Dirac operator chosen is far from elliptic; and a remarkable new trace discovered by Perrot replaces the operator trace. In its full form, Perrot’s theory constitutes a wholly new approach to index theory. The account presented here covers most but not all of his approach. 
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