Laplacians on smooth distributions as $C^{\ast }$-algebra multipliers

Abstract

In this paper we continue the study of spectral properties of Laplacians associated with an arbitrary smooth distribution on a compact manifold, initiated in a previous paper. Under assumption that the singular foliation generated by the distribution is smooth, we prove that the Laplacian associated with the distribution defines an unbounded regular self-adjoint operator in some Hilbert module over the foliation $C^{\ast }$-algebra.

References in corpus (2)

• Index theory and non-commutative geometry on foliated manifolds
• Laplacians on smooth distributions