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2010•arXiv (Cornell University)Open access

$L^1$ cohomology of bounded subanalytic manifolds

Guillaume Valette

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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 Poincaré dual to $L^\infty$ cohomology (in dimension $j

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What this paper is about

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 Poincaré dual to $L^\infty$ cohomology (in dimension $j

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Available 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 Poincaré dual to $L^\infty$ cohomology (in dimension $j

Key concepts: Mathematics, Cohomology, Poincaré duality, Bounded function, Submanifold, Pure mathematics, Gravitational singularity, Homology (biology)

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