Pseudodifferential calculus on a singular foliation

Abstract

In a previous paper ([1]), we associated a holonomy groupoid and a C*-algebra to any singular foliation $(M,\mathcal{F})$. Using these, we construct the associated pseudodifferential calculus. This calculus gives meaning to a Laplace operator of any singular foliation $\mathcal{F}$ on a compact manifold $M$, and we show that it can be naturally understood as a positive, unbounded, self-adjoint operator on $L^2(M)$.