Lipschitz homotopy convergence of Alexandrov spaces II
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866918326192570368 |
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| author | Fujioka, Tadashi Mitsuishi, Ayato Yamaguchi, Takao |
| author_facet | Fujioka, Tadashi Mitsuishi, Ayato Yamaguchi, Takao |
| contents | We establish a quantitative version of the Lipschitz homotopy convergence introduced by Mitsuishi and Yamaguchi for a moduli space of compact Alexandrov spaces without collapsing. Along the way, we obtain a Lipschitz version of Petersen's homotopy stability theorem that is applicable to more general settings, including CAT spaces. We also show that the Lipschitz homotopies can be chosen to preserve the singular strata of Alexandrov spaces, i.e., extremal subsets. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_12515 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Lipschitz homotopy convergence of Alexandrov spaces II Fujioka, Tadashi Mitsuishi, Ayato Yamaguchi, Takao Differential Geometry Metric Geometry 53C20, 53C23 We establish a quantitative version of the Lipschitz homotopy convergence introduced by Mitsuishi and Yamaguchi for a moduli space of compact Alexandrov spaces without collapsing. Along the way, we obtain a Lipschitz version of Petersen's homotopy stability theorem that is applicable to more general settings, including CAT spaces. We also show that the Lipschitz homotopies can be chosen to preserve the singular strata of Alexandrov spaces, i.e., extremal subsets. |
| title | Lipschitz homotopy convergence of Alexandrov spaces II |
| topic | Differential Geometry Metric Geometry 53C20, 53C23 |
| url | https://arxiv.org/abs/2304.12515 |