real analytic De Rahm cohomology

Ali Taghavi · science forum addict Joined: 14 May 2005 Posts: 73

Hello

Let M be a real analytic manifold,
consider the quotient of analytic closed form
by analytic exact forms (is this a finite dimensional vector space(with the same dimension of smooth cohomology)
Thank you
Ali Taghavi

Pierre-Yves Gaillard · science forum beginner Joined: 22 Jun 2005 Posts: 22

If a real analytic paracompact manifold admits an analytic riemannian
metric (I don't know if such is always the case), then the inclusion of
the complex of analytic forms into that of smooth forms induces a
Frechet isomorphism in cohomology by

http://www.iecn.u-nancy.fr/~gaillard/DIVERS/Hodge.Theorem/

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