The principal-symbol index map for an algebra of pseudodifferential operators
Differential Geometry
2019-05-07 v2 Operator Algebras
Abstract
A C*algebra A generated by a class of zero-order classical pseudodifferential operator on a cylinder RxB, where B is a compact riemannian manifold, containing operators with periodic symbols, is considered. A description of the K-theory index map associated to the continuous extension to A of the principal-symbol map is given. That index map takes values in K_0 of the commutator ideal E of the algebra, which is isomorphic to Z^2. It maps the K_1-class of an operator invertible modulo E to the Fredholm indices of a pair of elliptic pseudodifferentail operators on SxB, where S denotes the circle.
Cite
@article{arxiv.1901.10419,
title = {The principal-symbol index map for an algebra of pseudodifferential operators},
author = {Severino T. Melo},
journal= {arXiv preprint arXiv:1901.10419},
year = {2019}
}
Comments
To appear in: K-Theory in Algebra, Analysis and Topology. Only minor changes were made