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Journal of Mathematical Sciences

, Volume 201, Issue 6, pp 818–829 | Cite as

On the Index Formula for an Isometric Diffeomorphism

  • A. Yu Savin
  • B. Yu. Sternin
  • E. Schrohe
Article
  • 31 Downloads

Abstract

We give an elementary solution to the problem of the index of elliptic operators associated with shift operator along the trajectories of an isometric diffeomorphism of a smooth closed manifold. This solution is based on index-preserving reduction of the operator under consideration to some elliptic pseudo-differential operator on a higher-dimension manifold and on the application of the Atiyah–Singer formula. The final formula of the index is given in terms of the symbol of the operator on the original manifold.

Keywords

Manifold Elliptic Operator Noncommutative Geometry Topological Index Index Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Peoples’ Friendship University of RussiaMoscowRussia
  2. 2.Hannover Leibnitz-UniversitätHannoverGermany

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