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On the index formula for an isometric diffeomorphism. (English. Russian original) Zbl 1310.58014
J. Math. Sci., New York 201, No. 6, 818-829 (2014); translation from Sovrem. Mat., Fundam. Napravl. 46, 141-152 (2012).
Summary: 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.
MSC:
58J20 Index theory and related fixed-point theorems on manifolds
58J40 Pseudodifferential and Fourier integral operators on manifolds
58B34 Noncommutative geometry (à la Connes)
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