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1999 | 161 | 1-2 | 93-117
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Spaces of polynomials with roots of bounded multiplicity

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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.
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  • Department of Mathematics, University of Rochester, Rochester, NY 14627
  • Department of Mathematics, Tokyo Metropolitan University, Minami-Ohsawa 1-1, Hachioji-shi, Tokyo 192-0397, Japan
  • Department of Mathematics, Toyama International University, Kaminikawa, Toyama 930-1262, Japan
  • Department of Mathematics, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan
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