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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.

MSC:
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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