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Quelques propriétés des applications analytiques près d’un homéomorphisme. (French) Zbl 0579.32042
Suppose that \(\phi\) : \(V\to W\) is a homeomorphism between two (real or complex) analytic spaces. This paper is concerned with the question whether any analytic map \(\psi\) : \(V\to W\) sufficiently close to \(\phi\) must also be a homeomorphism. The author proves that if \(\psi\) : \(V\to W\) is an algebraic map between complex projective varieties which induces an isomorphism on integral homology then \(\psi\) is an algebraic isomorphism. It is also proved that if \(\psi\) is an analytic map between connected compact real analytic spaces which induces an isomorphism on \({\mathbb{Z}}_ 2\)-homology and if \(\psi\) restricts to an isomorphism from \(V-S\) to \(W- \psi (S)\) for some proper analytic subspace S of V, then \(\psi\) is a homeomorphism.
Reviewer: F.Kirwan
MSC:
32H99 Holomorphic mappings and correspondences
32C15 Complex spaces
14E05 Rational and birational maps
32C05 Real-analytic manifolds, real-analytic spaces
32J99 Compact analytic spaces
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