Work

$\ell^p$ metrics on cell complexes

Year: 2023

Type: preprint

Abstract: 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.

Source: HAL (Le Centre pour la Communication Scientifique Directe)

DOI: 10.48550/arxiv.2302.03801

Authors: Haettel, Thomas, Hoda, Nima, Petyt, Harry

Institutions: Centre National de la Recherche Scientifique, Université de Montpellier, University of Oxford, Institut Montpelliérain Alexander Grothendieck, Centre de recherches mathématiques, CRM-CNRS International Research Laboratory, Université de Montréal

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Agence Nationale de la Recherche, Natural Sciences and Engineering Research Council of Canada

Award: Groups acting on fractals

OpenAlex ID: W4319792403

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