Adiabatic limits and spectral sequences for Riemannian foliations
Abstract
For general Riemannian foliations, spectral asymptotics of the Laplacian is studied when the metric on the ambient manifold is blown up in directions normal to the leaves (adiabatic limit). The number of ``small'' eigenvalues is given in terms of the differentiable spectral sequence of the foliation. The asymptotics of the corresponding eigenforms also leads to a Hodge theoretic description of this spectral sequence. This is an extension of results of MazzeoMelrose and R. Forman.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 February 1999
 arXiv:
 arXiv:math/9902147
 Bibcode:
 1999math......2147A
 Keywords:

 Differential Geometry;
 Spectral Theory;
 58G25 (Primary) 58A14 53C12 57R30 (Secondary)
 EPrint:
 42 pages, LaTeX, using amssymb and amscd