English

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 CC^*-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