The index of projective families of elliptic operators
Varghese Mathai, Richard B Melrose, Isadore M Singer
Abstract
An index theory for projective families of elliptic pseudodifferential operators is developed. The topological and the analytic index of such a family both take values in twisted K-theory of the parametrizing space, X. The main result is the equality of these two notions of index when the twisting class is in the torsion subgroup of H3(X;Z). The Chern character of the index class is then computed.
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