Stable splitting of the space of polynomials with roots of bounded multiplicity

Guest, Martin A.; Kozłowski, Andrzej; Yamaguchi, Kohhei

doi:10.1215/kjm/1250518124

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Introduction2

Theorem 142

Previous Results1

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Cited by 17 publications

(19 citation statements)

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“…This is not surprising, because a similar result holds for several cases (e.g. [6,9]). Next, although the method of this paper is completely homotopy theoretic, this result might be explained by using Morse theoretical principle (cf.…”

Section: Introductionsupporting

confidence: 64%

Spaces of Free Loops on Real Projective Spaces

Yamaguchi

2005

Kyushu J. Math.

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Section: Introductionsupporting

confidence: 64%

Spaces of Free Loops on Real Projective Spaces

Yamaguchi

2005

Kyushu J. Math.

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“…Apart from those cited above, we should mention the results of Vassiliev [14], [15] and the work of Guest, Kozlowski and Yamaguchi [5]. It was pointed out by the referee that when m 3 our Proposition 4.1 is a particular case of Theorem 3.8 in [5]. We should also say that our main theorem follows from the results recently obtained in [8], [16] by Kozlowski and Yamaguchi.…”

Section: Theorem 14mentioning

confidence: 60%

“…Our methods and results are closely related to recent work on the complements of discriminants. Apart from those cited above, we should mention the results of Vassiliev [14], [15] and the work of Guest, Kozlowski and Yamaguchi [5]. It was pointed out by the referee that when m 3 our Proposition 4.1 is a particular case of Theorem 3.8 in [5].…”

Section: Theorem 14mentioning

confidence: 86%

Spaces of rational loops on a real projective space

Mostovoy¹

2001

Trans. Amer. Math. Soc.

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“…is proved in [9] and the second is proved in [7]. The condition n ≥ 3 in (2.3) implies that each space is simply connected.…”

Section: Previous Resultsmentioning

confidence: 92%

Relationship between polynomials with multiple roots and rational functions with common roots

Kamiyama¹

2005

MATH. SCAND.

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For F = R or C, let P l k,n (F ) denote the space of monic polynomials f (z) over F of degree k and such that the number of n-fold roots of f (z) is at most l. Let X l k,n (F ) denote the space consisting of all n-tuples (p 1 (z), . . . , p n (z)) of monic polynomials over F of degree k and such that there are at most l roots common to all p i (z). In this paper, we prove that(F ) are stably homotopy equivalent. In fact, they are homotopy equivalent when F = C and (n, l) = (2, 0). We also consider the case that n-fold roots and common roots are not real. These results generalize previous results concerning these spaces.

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Stable splitting of the space of polynomials with roots of bounded multiplicity

Cited by 17 publications

References 10 publications

Spaces of Free Loops on Real Projective Spaces

Spaces of Free Loops on Real Projective Spaces

Spaces of rational loops on a real projective space

Relationship between polynomials with multiple roots and rational functions with common roots

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