Hodge theory and cohomology with compact supports

Details Hodge theory and cohomology with compact supports Hodge theory and cohomology with compact supports

1998-04-28

arxiv.org/abs/math/9804152v1

Soochow Journal of Mathematics, vol 28 no. 1, 2002, 33--55

Mathematics

Differential Geometry

Scientific paper

This paper constructs a Hodge theory of noncompact topologically tame manifolds $M$. The main result is an isomorphism between the de Rham cohomology with compact supports of $M$ and the kernel of the Hodge--Witten--Bismut Laplacian $\lap_\mu$ associated to a measure $d\mu$ which has sufficiently rapid growth at infinity on $M$. This follows from the construction of a space of forms associated to $\lap_\mu$ which satisfy an ``extension by zero'' property. The ``extension by zero'' property is proved for manifolds with cylindrical ends possessing gaussian growth measures.

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