Laplacians and Spectrum for Singular Foliations  

作　　者：Iakovos ANDROULIDAKIS 

机构地区：[1]National and Kapodistrian University of Athens, Department of Mathematics, Panepistimiopolis, GR15784 Athens, Greece

出　　处：《Chinese Annals of Mathematics,Series B》2014年第5期679-690,共12页数学年刊（B辑英文版）

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

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.

关 键 词：LAPLACIAN Singular foliation HOLONOMY 

分 类 号：O177[理学—数学]