On weighted 𝐿² cohomology

Miller, John

doi:10.1090/S0002-9939-07-08920-4

On weighted $L^{2}$ cohomology
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by John G. Miller PDF

Proc. Amer. Math. Soc. 135 (2007), 4057-4061 Request permission

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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