C*-algebras and Elliptic Theory II

Part of the series Trends in Mathematics pp 123-144

Adiabatic Limits and the Spectrum of the Laplacian on Foliated Manifolds

  • Yuri A. KordyukovAffiliated withInstitute of Mathematics, Russian Academy of Sciences
  • , Andrey A. YakovlevAffiliated withDepartment of Mathematics, Ufa State Aviation Technical University

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We present some recent results on the behavior of the spectrum of the differential form Laplacian on a Riemannian foliated manifold when the metric on the ambient manifold is blown up in directions normal to the leaves (in the adiabatic limit).