Russian Journal of Mathematical Physics

, Volume 22, Issue 3, pp 410–420 | Cite as

Uniformization and index of elliptic operators associated with diffeomorphisms of a manifold

  • A. SavinEmail author
  • E. Schrohe
  • B. Sternin


We consider the index problem for a wide class of nonlocal elliptic operators on a smooth closed manifold, namely, differential operators with shifts induced by the action of a (not necessarily periodic) isometric diffeomorphism. The key to the solution is the method of uniformization. To the nonlocal problem we assign a pseudodifferential operator, with the same index, acting on the sections of an infinite-dimensional vector bundle on a compact manifold. We then determine the index in terms of topological invariants of the symbol, using the Atiyah—Singer index theorem.


Vector Bundle Elliptic Operator Fredholm Operator Noncommutative Geometry Topological Index 
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© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Peoples’ Friendship University of RussiaMoscowRussia
  2. 2.Institut für Analysis GottfriedWilhelm Leibniz UniversitätHannoverDeutschland

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