The index of projective families of elliptic operators

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 $H^3\left(X;\mathbb{Z}\right)$. The Chern character of the index class is then computed.