Annali dell’Università di Ferrara

, Volume 40, Issue 1, pp 23–30 | Cite as

An analytic version of the De Rham theorem

  • Lucia Beretta


LetV be a real analytic paracompact variety; in §1 of this paper we prove that:
$$H^q (V,R) \approx \frac{{closed analytic differentiable q - forms on V}}{{exact analytic differentiable q - forms on V}}$$
Then we prove that the closed (exact) analytic differentiableq-forms onV are dense, in the Whitney topology, in the set of closed (exact) differentiableq-forms onV. We also consider the problem of extending closed (exact) analytic differentiableq-forms, defined on a subvarietyX ofV, to closed (exact) analytic forms defined onV.


Exact Sequence Cohomology Class Approximation Theorem Natural Isomorphism Coherent Sheave 
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SiaV una varietà analitica reale paracompatta; nel § 1 di questo articolo si prova che:
$$H^q (V,R) \approx \frac{{q - forme differenziali analitiche chiuse su V}}{{q - forme differenziali analitiche esatte su V}}$$
Nel seguito si dimostra che leq-forme analitiche chiuse (esatte) suV sono dense, nella topologia di Whitney, nelleq-forme differenziali chiuse (esatte) suV. Si prende anche in considerazione il problema di estendereq-forme differenziali analitiche chiuse (esatte), definite su una sottovarietàX diV, a forme analitiche chiuse (esatte) definite suV.


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Copyright information

© Università degli Studi di Ferrara 1994

Authors and Affiliations

  • Lucia Beretta
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di TrentoPovo (TN)

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