On approximation of smooth submanifolds by nonsingular real algebraic subvarieties
Jacek Bochnak, Wojciech Kucharz (2003)
Annales scientifiques de l'École Normale Supérieure
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Jacek Bochnak, Wojciech Kucharz (2003)
Annales scientifiques de l'École Normale Supérieure
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Nicholaas H. Kuiper (1967)
Publications Mathématiques de l'IHÉS
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C. Bowszyc (1983)
Fundamenta Mathematicae
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Wojciech Kucharz (1986)
Compositio Mathematica
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A. Van de Ven (1985-1986)
Séminaire Bourbaki
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A. Tognoli (1979-1980)
Séminaire Bourbaki
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Alberto Tognoli (2003)
Bollettino dell'Unione Matematica Italiana
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We study the problem of approximating, up to homotopy, compact topological manifolds by real algebraic varieties. As a consequence, we realize any integral non-degenerate quadratic form as the intersection form of a real algebraic variety. This is related to a well-known result, due to Freedman [F], on the topology of closed simply-connected topological -manifolds.