تقرير
$\ell^p$ metrics on cell complexes
العنوان: | $\ell^p$ metrics on cell complexes |
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المؤلفون: | Haettel, Thomas, Hoda, Nima, Petyt, Harry |
سنة النشر: | 2023 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Group Theory, Mathematics - Metric Geometry, 57M60, 52A21, 51F30, 20F65, 20F67 |
الوصف: | 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. Comment: 36 pages, 7 figures |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/2302.03801 |
رقم الأكسشن: | edsarx.2302.03801 |
قاعدة البيانات: | arXiv |
الوصف غير متاح. |