Continuous rational maps into spheres
Algebraic Geometry
2016-02-08 v3
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.
Cite
@article{arxiv.1403.5127,
title = {Continuous rational maps into spheres},
author = {Wojciech Kucharz},
journal= {arXiv preprint arXiv:1403.5127},
year = {2016}
}
Comments
To appear in Mathematische Zeitschrift