On the Homotopy Classification of Elliptic Operators on Manifolds with Edges
Operator Algebras
2015-06-26 v1 Analysis of PDEs
K-Theory and Homology
Abstract
We obtain a classification of elliptic operators modulo stable homotopy on manifolds with edges (this is in some sense the simplest class of manifolds with nonisolated singularities). We show that the operators are classified by the K-homology group of the manifold. To this end, we construct exact sequence in elliptic theory isomorphic to the K-homology exact sequence. The main part of the proof is the computation of the boundary map using semiclassical quantization.
Keywords
Cite
@article{arxiv.math/0503694,
title = {On the Homotopy Classification of Elliptic Operators on Manifolds with Edges},
author = {V. Nazaikinskii and A. Savin and B. -W. Schulze and B. Sternin},
journal= {arXiv preprint arXiv:math/0503694},
year = {2015}
}