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Annali dell’Università di Ferrara

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

An analytic version of the De Rham theorem

  • Lucia Beretta
Article
  • 12 Downloads

Abstract

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.

Keywords

Exact Sequence Cohomology Class Approximation Theorem Natural Isomorphism Coherent Sheave 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Sunto

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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References

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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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