Index of elliptic operators for a diffeomorphism
Operator Algebras
2015-11-06 v1 Analysis of PDEs
K-Theory and Homology
Abstract
We develop elliptic theory of 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 of 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.
Keywords
Cite
@article{arxiv.1106.4195,
title = {Index of elliptic operators for a diffeomorphism},
author = {Anton Savin and Boris Sternin},
journal= {arXiv preprint arXiv:1106.4195},
year = {2015}
}
Comments
37 pages