On the Index Formula for an Isometric Diffeomorphism
Analysis of PDEs
2011-12-26 v1 Dynamical Systems
Functional Analysis
K-Theory and Homology
Abstract
We give an elementary solution of the index problem for elliptic operators associated with the shift operator along the trajectories of an isometric diffeomorphism of a closed smooth manifold. This solution is based on a reduction (which preserves the index) of the operator to an elliptic pseudodifferential operator on a manifold of a higher dimension and an application of an Atiyah--Singer type formula. The final index formula is given in terms of the symbol of the operator on the original manifold.
Cite
@article{arxiv.1112.5515,
title = {On the Index Formula for an Isometric Diffeomorphism},
author = {A. Savin and E. Schrohe and B. Sternin},
journal= {arXiv preprint arXiv:1112.5515},
year = {2011}
}
Comments
16 pages