Submanifolds of real algebraic varieties

Kucharz, W.

doi:10.1090/S0002-9939-07-08944-7

Submanifolds of real algebraic varieties
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Proc. Amer. Math. Soc. 136 (2008), 55-60 Request permission

Abstract:

By the Nash-Tognoli theorem, each compact smooth manifold $M$ is diffeomorphic to a nonsingular real algebraic set, called an algebraic model of $M$. We construct algebraic models $X$ of $M$ with controlled behavior of the group of cohomology classes represented by algebraic subsets of $X$.

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