Coarse Geometry of Free Products of Metric Spaces
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866910949933318144 |
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| author | Wang, Qin Yao, Jvbin |
| author_facet | Wang, Qin Yao, Jvbin |
| contents | Recently, a notion of the free product $X \ast Y$ of two metric spaces $X$ and $Y$ has been introduced by T. Fukaya and T. Matsuka. In this paper, we study coarse geometric permanence properties of the free product $X \ast Y$. We show that if $X$ and $Y$ satisfy any of the following conditions, then $X \ast Y$ also satisfies that condition: (1) they are coarsely embeddable into a Hilbert space or a uniformly convex Banach space; (2) they have Yu's Property A; (3) they are hyperbolic spaces. These generalize the corresponding results for discrete groups to the case of metric spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_04118 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coarse Geometry of Free Products of Metric Spaces Wang, Qin Yao, Jvbin Functional Analysis Metric Geometry Recently, a notion of the free product $X \ast Y$ of two metric spaces $X$ and $Y$ has been introduced by T. Fukaya and T. Matsuka. In this paper, we study coarse geometric permanence properties of the free product $X \ast Y$. We show that if $X$ and $Y$ satisfy any of the following conditions, then $X \ast Y$ also satisfies that condition: (1) they are coarsely embeddable into a Hilbert space or a uniformly convex Banach space; (2) they have Yu's Property A; (3) they are hyperbolic spaces. These generalize the corresponding results for discrete groups to the case of metric spaces. |
| title | Coarse Geometry of Free Products of Metric Spaces |
| topic | Functional Analysis Metric Geometry |
| url | https://arxiv.org/abs/2505.04118 |