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Spaces of polynomials with roots of bounded multiplicity. (English) Zbl 1016.55004
Summary: We describe an alternative approach to some results of V. A. Vassiliev [Complements of discriminants of smooth maps: topology and applications, Transl. Math. Monographs 98, Am. Math. Soc. (1992; Zbl 0762.55001)] on spaces of polynomials, by applying the “scanning method” used by G. Segal [Acta Math. 143, 39-72 (1979; Zbl 0427.55006)] 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.

55P15 Classification of homotopy type
57R45 Singularities of differentiable mappings in differential topology
55P35 Loop spaces
58D15 Manifolds of mappings
55R80 Discriminantal varieties and configuration spaces in algebraic topology
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