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arXiv · 1403.5127

Continuous rational maps into spheres

Wojciech Kucharz
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Abstract

Let X be a compact nonsingular real algebraic variety. We prove that if a continuous map from X into the unit p-sphere is homotopic to a continuous rational map, then, under certain assumptions, it can be approximated in the compact-open topology by continuous rational maps. As a byproduct, we also obtain some results on approximation of smooth submanifolds by nonsingular subvarieties.

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Wojciech Kucharz. 2016-02-05. Continuous rational maps into spheres. https://doi.org/10.1007/s00209-016-1634-4

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