$L^1$ cohomology of bounded subanalytic manifolds

Details $L^1$ cohomology of bounded subanalytic manifolds $L^1$ cohomology of bounded subanalytic manifolds

2010-11-09

arxiv.org/abs/1011.2023v1

Mathematics

Algebraic Geometry

36 pages

Scientific paper

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 Poincar\'e dual to $L^\infty$ cohomology (in dimension $j

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