Mathematische Zeitschrift

, Volume 250, Issue 1, pp 43–57 | Cite as

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

  • Junya TakahashiEmail author


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.


Riemannian Manifold Large Eigenvalue Cohomology Group Positive Eigenvalue Generic Fiber 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  1. 1.Division of Mathematics, Graduate School of Information SciencesTôhoku UniversitySendaiJapan

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