In a previous paper (), we associated a holonomy groupoid and a C*-algebra to any singular foliation (M,ℱ). Using these, we construct the associated pseudodifferential calculus. This calculus gives meaning to a Laplace operator of any singular foliation ℱ on a compact manifold M, and we show that it can be naturally understood as a positive, unbounded, self-adjoint operator on L2(M).
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Iakovos Androulidakis, Georges Skandalis, Pseudodifferential calculus on a singular foliation. J. Noncommut. Geom. 5 (2011), no. 1, pp. 125–152DOI 10.4171/JNCG/72