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| Laplacians and Spectrum for Singular Foliations |
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Citation： |
Iakovos ANDROULIDAKIS.Laplacians and Spectrum for Singular Foliations[J].Chinese Annals of Mathematics B,2014,35(5):679~690 |
| Page view： 1260
Net amount： 1062 |
Authors： |
Iakovos ANDROULIDAKIS; |
Foundation： |
Marie Curie Career Integration Grant (No. FP7-PEOPLE-2011-CIG,
No. PCI09-GA-2011-290823) and the FCT (Portugal) with European Regional Development Fund
(COMPETE) and national funds through the project PTDC/MAT/098770/2008. |
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| Abstract： |
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. |
Keywords： |
Laplacian, Singular foliation, Holonomy |
Classification： |
53C12, 35J05, 47A10, 53C29, 22A22 |
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