### Abstract

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.

Original language | English |
---|---|

Pages (from-to) | 93-117 |

Number of pages | 25 |

Journal | Fundamenta Mathematicae |

Volume | 161 |

Issue number | 1-2 |

Publication status | Published - 2000 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Fundamenta Mathematicae*,

*161*(1-2), 93-117.

**Spaces of polynomials with roots of bounded-multiplicity.** / Guest, Martin; Kozlowski, A.; Yamaguchi, K.

Research output: Contribution to journal › Article

*Fundamenta Mathematicae*, vol. 161, no. 1-2, pp. 93-117.

}

TY - JOUR

T1 - Spaces of polynomials with roots of bounded-multiplicity

AU - Guest, Martin

AU - Kozlowski, A.

AU - Yamaguchi, K.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0039003874&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0039003874&partnerID=8YFLogxK

M3 - Article

VL - 161

SP - 93

EP - 117

JO - Fundamenta Mathematicae

JF - Fundamenta Mathematicae

SN - 0016-2736

IS - 1-2

ER -