Laplacians on generalized smooth distributions as $C^*$-algebra multipliers
Differential Geometry
2019-02-11 v1 Operator Algebras
Abstract
In this paper, we discuss spectral properties of Laplacians associated with an arbitrary smooth distribution on a compact manifold. First, we give a survey of results on generalized smooth distributions on manifolds, Riemannian structures and associated Laplacians. Then, under the assumption that the singular foliation generated by the distribution is regular, we prove that the Laplacian associated with the distribution defines an unbounded multiplier on the foliation -algebra. To this end, we give the construction of a parametrix.
Keywords
Cite
@article{arxiv.1902.03139,
title = {Laplacians on generalized smooth distributions as $C^*$-algebra multipliers},
author = {Iakovos Androulidakis and Yuri A. Kordyukov},
journal= {arXiv preprint arXiv:1902.03139},
year = {2019}
}
Comments
19 pages. arXiv admin note: text overlap with arXiv:1710.10119, arXiv:1807.06815