Geometry & Topology

The index of projective families of elliptic operators

Varghese Mathai, Richard B Melrose, and Isadore M Singer

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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;). The Chern character of the index class is then computed.

Article information

Geom. Topol., Volume 9, Number 1 (2005), 341-373.

Received: 7 December 2004
Accepted: 28 February 2005
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 19K56: Index theory [See also 58J20, 58J22]
Secondary: 58J20: Index theory and related fixed point theorems [See also 19K56, 46L80]

projective vector bundles twisted $K$–theory projective families of elliptic operators Index theorem determinant lines twisted Chern character


Mathai, Varghese; Melrose, Richard B; Singer, Isadore M. The index of projective families of elliptic operators. Geom. Topol. 9 (2005), no. 1, 341--373. doi:10.2140/gt.2005.9.341.

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