Homotopy stability of spaces of non-resultant systems of bounded multiplicity with real coefficients
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866913856110985216 |
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| author | Kozlowski, Andrzej Yamaguchi, Kohhei |
| author_facet | Kozlowski, Andrzej Yamaguchi, Kohhei |
| contents | 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 $m n =3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_00307 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Homotopy stability of spaces of non-resultant systems of bounded multiplicity with real coefficients Kozlowski, Andrzej Yamaguchi, Kohhei Algebraic Topology 55P15, 55R80, 55P35 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 $m n =3$. |
| title | Homotopy stability of spaces of non-resultant systems of bounded multiplicity with real coefficients |
| topic | Algebraic Topology 55P15, 55R80, 55P35 |
| url | https://arxiv.org/abs/2305.00307 |