Characteristic Classes and Zeroth Order Pseudodifferential Operators
Differential Geometry
2010-05-27 v2 Analysis of PDEs
Algebraic Topology
Abstract
We provide evidence for the conjecture that the Wodzicki-Chern classes vanish for all bundles with the group Z of invertible zeroth order pseudodifferential operators as structure group. In particular, we prove this vanishing if the structure group reduces to pseudodifferential operators with leading order symbol the identity. The leading order Chern classes are nonzero in general, and they detect elements of the de Rham cohomology groups of the classifying space BZ.
Cite
@article{arxiv.1003.0067,
title = {Characteristic Classes and Zeroth Order Pseudodifferential Operators},
author = {Andrés Larrain-Hubach and Steven Rosenberg and Simon Scott and Fabián Torres-Ardila},
journal= {arXiv preprint arXiv:1003.0067},
year = {2010}
}
Comments
Second version contains improved exposition and results. To appear in Contemporary Mathematics