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- W1521662128 abstract "We prove some de Rham theorems on bounded subanalytic submanifolds of $R^n$ (not necessarily compact). We show that the $L^1$ cohomology of such a submanifold is isomorphic to its singular homology. In the case where the closure of the underlying manifold has only isolated singularities this implies that the $L^1$ cohomology is Poincare dual to $L^infty$ cohomology (in dimension $j <m-1$). In general, Poincare duality is related to the so-called $L^1$ Stokes' Property. For oriented manifolds, we show that the $L^1$ Stokes' property holds if and only if integration realizes a nondegenerate pairing between $L^1$ and $L^infty$ forms. This is the counterpart of a theorem proved by Cheeger on $L^2$ forms." @default.
- W1521662128 created "2016-06-24" @default.
- W1521662128 creator A5067470130 @default.
- W1521662128 date "2010-11-09" @default.
- W1521662128 modified "2023-09-27" @default.
- W1521662128 title "$L^1$ cohomology of bounded subanalytic manifolds" @default.
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