Adiabatic limits and spectral sequences for Riemannian foliations
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arXiv
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| Format: | Preprint |
| Published: |
1999
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| _version_ | 1866915287366893568 |
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| author | Lopez, Jesus A. Alvarez Kordyukov, Yuri A. |
| author_facet | Lopez, Jesus A. Alvarez Kordyukov, Yuri A. |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_math_9902147 |
| institution | arXiv |
| publishDate | 1999 |
| record_format | arxiv |
| spellingShingle | Adiabatic limits and spectral sequences for Riemannian foliations Lopez, Jesus A. Alvarez Kordyukov, Yuri A. Differential Geometry Spectral Theory 58G25 (Primary) 58A14 53C12 57R30 (Secondary) 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. |
| title | Adiabatic limits and spectral sequences for Riemannian foliations |
| topic | Differential Geometry Spectral Theory 58G25 (Primary) 58A14 53C12 57R30 (Secondary) |
| url | https://arxiv.org/abs/math/9902147 |