Cycles on Nash algebraic models of smooth manifolds

Kucharz, Wojciech

doi:10.1090/S0002-9939-09-09663-4

Cycles on Nash algebraic models of smooth manifolds
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Proc. Amer. Math. Soc. 137 (2009), 1899-1906 Request permission

Abstract:

A Nash algebraic model of a compact smooth manifold $M$ is a pair $(X,X_0)$ where $X$ is a nonsingular real algebraic set and $X_0$ is the union of some connected components of $X$ such that $X_0$ is diffeomorphic to $M$. We study the homology classes on $X_0$ represented by algebraic subsets of $X$ contained in $X_0$ for various Nash algebraic models $(X,X_0)$ of $M$.

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