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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On weighted $ L^{2}$ cohomology


Author: John G. Miller
Journal: Proc. Amer. Math. Soc. 135 (2007), 4057-4061
MSC (2000): Primary 58J22
Published electronically: September 7, 2007
MathSciNet review: 2341958
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Abstract: Consider an orientable manifold with countably many complete components of bounded dimension. Suppose that its rational homology is infinitely generated in some degree. Then there is no choice of weight function for which the natural map from weighted $ L^{2}$ cohomology to de Rham cohomology is surjective in that degree.


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Additional Information

John G. Miller
Affiliation: Department of Mathematical Sciences, Indiana University-Purdue University at Indianapolis, Indianapolis, Indiana 46202-3216
Email: jmiller@math.iupui.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08920-4
PII: S 0002-9939(07)08920-4
Received by editor(s): July 5, 2006
Received by editor(s) in revised form: September 11, 2006
Published electronically: September 7, 2007
Communicated by: Mikhail Shubin
Article copyright: © Copyright 2007 American Mathematical Society