Journal of Noncommutative Geometry


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Volume 8, Issue 3, 2014, pp. 695–734
DOI: 10.4171/JNCG/168

Published online: 2014-09-15

Index of elliptic operators for diffeomorphisms of manifolds

Anton Savin[1] and Boris Sternin[2]

(1) Peoples’ Friendship University of Russia, Moscow
(2) Peoples’ Friendship University of Russia, Moscow

We develop an elliptic theory for operators associated with a diffeomorphism of a closed smooth manifold. The aim of the present paper is to obtain an index formula for such operators in terms of topological invariants of the manifold and the symbol of the operator. The symbol in this situation is an element of a certain crossed product. We express the index as the pairing of the class in K-theory defined by the symbol and the Todd class in periodic cyclic cohomology of the crossed product.

Keywords: Noncommutative elliptic theory, index, cyclic cohomology, crossed product, Haefliger cohomology, Todd class

Savin Anton, Sternin Boris: Index of elliptic operators for diffeomorphisms of manifolds. J. Noncommut. Geom. 8 (2014), 695-734. doi: 10.4171/JNCG/168