We describe an alternative approach to some results of Vassiliev ([Va1]) on spaces of polynomials, by applying the "scanning method" used by Segal ([Se2]) in his investigation of spaces of rational functions. We explain how these two approaches are related by the Smale-Hirsch Principle or the h-Principle of Gromov. We obtain several generalizations, which may be of interest in their own right.
@article{bwmeta1.element.bwnjournal-article-fmv161i1p93bwm,
author = {M. Guest and A. Kozlowski and K. Yamaguchi},
title = {Spaces of polynomials with roots of bounded multiplicity},
journal = {Fundamenta Mathematicae},
volume = {159},
year = {1999},
pages = {93-117},
zbl = {1016.55004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv161i1p93bwm}
}
Guest, M.; Kozlowski, A.; Yamaguchi, K. Spaces of polynomials with roots of bounded multiplicity. Fundamenta Mathematicae, Tome 159 (1999) pp. 93-117. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv161i1p93bwm/
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