$\ell^p$ metrics on cell complexes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916581895831552 |
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| author | Haettel, Thomas Hoda, Nima Petyt, Harry |
| author_facet | Haettel, Thomas Hoda, Nima Petyt, Harry |
| contents | Motivated by the observation that groups can be effectively studied using metric spaces modelled on $\ell^1$, $\ell^2$, and $\ell^\infty$ geometry, we consider cell complexes equipped with an $\ell^p$ metric for arbitrary $p$. Under weak conditions that can be checked locally, we establish nonpositive curvature properties of these complexes, such as Busemann-convexity and strong bolicity. We also provide detailed information on the geodesics of these metrics in the special case of CAT(0) cube complexes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2302_03801 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | $\ell^p$ metrics on cell complexes Haettel, Thomas Hoda, Nima Petyt, Harry Group Theory Metric Geometry 57M60, 52A21, 51F30, 20F65, 20F67 Motivated by the observation that groups can be effectively studied using metric spaces modelled on $\ell^1$, $\ell^2$, and $\ell^\infty$ geometry, we consider cell complexes equipped with an $\ell^p$ metric for arbitrary $p$. Under weak conditions that can be checked locally, we establish nonpositive curvature properties of these complexes, such as Busemann-convexity and strong bolicity. We also provide detailed information on the geodesics of these metrics in the special case of CAT(0) cube complexes. |
| title | $\ell^p$ metrics on cell complexes |
| topic | Group Theory Metric Geometry 57M60, 52A21, 51F30, 20F65, 20F67 |
| url | https://arxiv.org/abs/2302.03801 |