Volume 9, issue 1 (2005)

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The index of projective families of elliptic operators

Varghese Mathai, Richard B Melrose and Isadore M Singer

Geometry & Topology 9 (2005) 341–373
 arXiv: math.DG/0206002
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 ${H}^{3}\left(X;ℤ\right)$. The Chern character of the index class is then computed.

Keywords
projective vector bundles, twisted $K$–theory, projective families of elliptic operators, Index theorem, determinant lines, twisted Chern character
Primary: 19K56
Secondary: 58J20