摘要
The author surveys Connes' results on the longitudinal Laplace operator along a(regular) foliation and its spectrum, and discusses their generalization to any singular foliation on a compact manifold. Namely, it is proved that the Laplacian of a singular foliation is an essentially self-adjoint operator(unbounded) and has the same spectrum in every(faithful) representation, in particular, in L2 of the manifold and L2 of a leaf.The author also discusses briefly the relation of the Baum-Connes assembly map with the calculation of the spectrum.
基金
supported by a Marie Curie Career Integration Grant(No.FP7-PEOPLE-2011-CIG,No.PCI09-GA-2011-290823)
the FCT(Portugal)with European Regional Development Fund(COMPETE)
national funds through the project PTDC/MAT/098770/2008
