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Displaying similar documents to “Real algebraic structures on topological spaces”

Classification of Nash manifolds

Masahiro Shiota (1983)

Annales de l'institut Fourier

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A semi-algebraic analytic manifold and a semi-algebraic analytic map are called a Nash manifold and a Nash map respectively. We clarify the category of Nash manifolds and Nash maps.

Topological manifolds and real algebraic geometry

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 4 -manifolds.