The homotopy type of spaces of real resultants with bounded multiplicity

2018/03/06 by Kozlowski, Andrzej, Yamaguchi, Kohhei
#55P10 #55R80 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1803.02154

Abstract

For positive integers d,m,n≥ 1 with (m,n)\not= (1,1) and \Bbb K=\Bbb R or \Bbb C, let Q^d,m_n(\Bbb K) denote the space of m-tuples (f₁(z),⋯ ,f_m(z))∈ \Bbb K [z]^m of \Bbb K-coefficients monic polynomials of the same degree d such that polynomials \f_k(z)\_k=1^m have no common \it real root of multiplicity ≥ n (but may have complex common root of any multiplicity). %% These spaces can be regarded as one of generalizations of the spaces defined and studied by Arnold and Vassiliev, and they may be also considered as the real analogues of the spaces studied by B. Farb and J. Wolfson. In this paper, we shall determine their homotopy types explicitly and generalize some previously obtained results.

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• The homotopy type of spaces of resultants of bounded multiplicity
• Spaces of non-resultant systems of bounded multiplicity with real coefficients
• Homotopy stability of spaces of non-resultant systems of bounded multiplicity with real coefficients
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