Homotopy stability of spaces of non-resultant systems of bounded multiplicity with real coefficients

2023/04/29 by A. Kozłowski, Kozlowski, Andrzej, Kohhei Yamaguchi +1
Mathematics · #55P15 #55P35 #55R80 #Advanced Topics in Algebra #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2305.00307

openalex publication_date 2023/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We continue our study of the topology of the spaces of m tuples of real polynomials with common degree d and without common roots of multiplicity n, and in particular their stability properties with respect to d. In an earlier paper we have proved a homotopy stability result and determined the stable homotopy types of such spaces in the case m n >=4. In the case m n= 3 we could only prove stability in homology. In this paper we prove the corresponding homotopy result for the case m n =3.

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