Vanishing of cohomology groups and large eigenvalues of the Laplacian on p-forms

Junya Takahashi

doi:10.1007/s00209-004-0735-z

Vanishing of cohomology groups and large eigenvalues of the Laplacian on p-forms

Junya Takahashi

INF - System Information Sciences

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

For collapsing of closed Riemannian manifolds, the first positive eigenvalue of the Laplacian on p-forms may or may not tend to infinity. In special cases, we show that the existence of the first positive eigenvalue tending to infinity is related to vanishing of cohomology groups of generic fibers.

Original language	English
Pages (from-to)	43-57
Number of pages	15
Journal	Mathematische Zeitschrift
Volume	250
Issue number	1
DOIs	https://doi.org/10.1007/s00209-004-0735-z
Publication status	Published - 2005 May 1

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s00209-004-0735-z

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title = "Vanishing of cohomology groups and large eigenvalues of the Laplacian on p-forms",

abstract = "For collapsing of closed Riemannian manifolds, the first positive eigenvalue of the Laplacian on p-forms may or may not tend to infinity. In special cases, we show that the existence of the first positive eigenvalue tending to infinity is related to vanishing of cohomology groups of generic fibers.",

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Vanishing of cohomology groups and large eigenvalues of the Laplacian on p-forms

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