ℓp$\ell ^p$ metrics on cell complexes
Abstract Motivated by the observation that groups can be effectively studied using metric spaces modelled on , and geometry, we consider cell complexes equipped with an metric for arbitrary . Under weak conditions that can be checked locally, we establish non‐positive 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.
Authors
- Harry Petyt
- Thomas Haettel (ORCID: https://orcid.org/0000-0002-9395-1483)
- Nima Hoda (ORCID: https://orcid.org/0000-0002-6308-7751)
Institutions
- Centre National de la Recherche Scientifique (FR)
- Université de Montpellier (FR)
- Cornell University (US)
- Université Paris Sciences et Lettres (FR)
- University of Oxford (GB)
- Université de Montréal (CA)
Publication Details
- Journal
- Journal of the London Mathematical Society
- Published
- 2024-12-27
- DOI
- https://doi.org/10.1112/jlms.70062
- Citations
- 3
- Primary Topic
- Advanced Operator Algebra Research
- Type
- article
- Field-Weighted Citation Impact
- 2.67
Funders
- Agence Nationale de la Recherche
- Natural Sciences and Engineering Research Council of Canada
- European Research Council