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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Analyticity of homology classes

Author: Alberto Tognoli
Journal: Proc. Amer. Math. Soc. 104 (1988), 920-922
MSC: Primary 57R95; Secondary 32C05
MathSciNet review: 964874
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Abstract: Let $ W$ be a real analytic manifold and $ \{ \alpha \} \in {H_p}(W,{Z_2})$. We shall say that $ \{ \alpha \} $ is analytic if there exists a compact analytic subset $ S$ of $ W$, such that: $ \{ \alpha \}=$   fundamental class of $S$$ \}$. The purpose of this short paper is to prove

Theorem 1. Let $ W$ be a paracompact real analytic manifold; then any homology class $ \{ \alpha \} \in {H_p}(W,{Z_2})$ is analytic.

We remember that a similar result does not hold in the real algebraic case (see [1]).

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PII: S 0002-9939(1988)0964874-2
Article copyright: © Copyright 1988 American Mathematical Society

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