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Some New Results on L2 Cohomology of Negatively Curved Riemannian Manifolds

Published online by Cambridge University Press:  20 November 2018

M. Cocos
M. Cocos*
Affiliation:
Department of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A., e-mail: cocos@math.umn.edu
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Abstract

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The present paper is concerned with the study of the ${{L}^{2}}$ cohomology spaces of negatively curved manifolds. The first half presents a finiteness and vanishing result obtained under some curvature assumptions, while the second half identifies a class of metrics having non-trivial ${{L}^{2}}$ cohomology for degree equal to the half dimension of the space. For the second part we rely on the existence and regularity properties of the solution for the heat equation for forms.

Keywords

58J50
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 57 , Issue 2 , 01 April 2005 , pp. 251 - 266
Copyright
Copyright © Canadian Mathematical Society 2005

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