## Geometry & Topology

### 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 $H3(X;ℤ)$. The Chern character of the index class is then computed.

#### Article information

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

Dates
Accepted: 28 February 2005
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.gt/1513799569

Digital Object Identifier
doi:10.2140/gt.2005.9.341

Mathematical Reviews number (MathSciNet)
MR2140985

Zentralblatt MATH identifier
1083.58021

#### Citation

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. https://projecteuclid.org/euclid.gt/1513799569

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