Hodge Theory and Cohomology with Compact Supports
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چکیده
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 △μ associated to a measure dμ which has sufficiently rapid growth at infinity on M . This follows from the construction of a space of forms associated to △μ 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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تاریخ انتشار 1998