{"title":"ℓ\u0000 p\u0000 \u0000 $ell ^p$\u0000 metrics on cell complexes","authors":"Thomas Haettel, Nima Hoda, Harry Petyt","doi":"10.1112/jlms.70062","DOIUrl":"https://doi.org/10.1112/jlms.70062","url":null,"abstract":"<p>Motivated by the observation that groups can be effectively studied using metric spaces modelled on <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>ℓ</mi>\u0000 <mn>1</mn>\u0000 </msup>\u0000 <annotation>$ell ^1$</annotation>\u0000 </semantics></math>, <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>ℓ</mi>\u0000 <mn>2</mn>\u0000 </msup>\u0000 <annotation>$ell ^2$</annotation>\u0000 </semantics></math> and <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>ℓ</mi>\u0000 <mi>∞</mi>\u0000 </msup>\u0000 <annotation>$ell ^infty$</annotation>\u0000 </semantics></math> geometry, we consider cell complexes equipped with an <span></span><math>\u0000 <semantics>\u0000 <msup>\u0000 <mi>ℓ</mi>\u0000 <mi>p</mi>\u0000 </msup>\u0000 <annotation>$ell ^p$</annotation>\u0000 </semantics></math> metric for arbitrary <span></span><math>\u0000 <semantics>\u0000 <mi>p</mi>\u0000 <annotation>$p$</annotation>\u0000 </semantics></math>. 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.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":"111 1","pages":""},"PeriodicalIF":1.0,"publicationDate":"2024-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.70062","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143119997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}