JournalsjncgVol. 8, No. 3pp. 695–734

Index of elliptic operators for diffeomorphisms of manifolds

  • Anton Savin

    Peoples’ Friendship University of Russia, Moscow
  • Boris Sternin

    Peoples’ Friendship University of Russia, Moscow
Index of elliptic operators for diffeomorphisms of manifolds cover
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Abstract

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.

Cite this article

Anton Savin, Boris Sternin, Index of elliptic operators for diffeomorphisms of manifolds. J. Noncommut. Geom. 8 (2014), no. 3, pp. 695–734

DOI 10.4171/JNCG/168