Adiabatic limits and spectral sequences for Riemannian foliations

Details Adiabatic limits and spectral sequences for Riemannian foliations Adiabatic limits and spectral sequences for Riemannian foliations

1999-02-25

arxiv.org/abs/math/9902147v1

Mathematics

Differential Geometry

42 pages, LaTeX, using amssymb and amscd

Scientific paper

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 Mazzeo-Melrose and R. Forman.

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