Homology of real algebraic varieties and morphisms to spheres

Öztürk, Alı̇

doi:10.1090/S0002-9939-08-09600-7

Homology of real algebraic varieties and morphisms to spheres
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Proc. Amer. Math. Soc. 137 (2009), 505-509 Request permission

Abstract:

Let $X$ and $Y$ be affine nonsingular real algebraic varieties. One of the classical problems in real algebraic geometry is whether a given $C^\infty$ mapping $f:X\rightarrow Y$ can be approximated by entire rational mappings in the space of $C^\infty$ mappings. In this work, we obtain some sufficient conditions in the case when $Y$ is the standard sphere $S^n$.

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