{"paper":{"title":"A combinatorial higher-rank hyperbolicity condition","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.MG","authors_text":"Martina J{\\o}rgensen, Urs Lang","submitted_at":"2022-06-16T13:17:07Z","abstract_excerpt":"We investigate a coarse version of a $2(n+1)$-point inequality characterizing metric spaces of combinatorial dimension at most $n$ due to Dress. This condition, experimentally called $(n,\\delta)$-hyperbolicity, reduces to Gromov's quadruple definition of $\\delta$-hyperbolicity in case $n = 1$. The $l_\\infty$-product of $n$ $\\delta$-hyperbolic spaces is $(n,\\delta)$-hyperbolic. Every $(n,\\delta)$-hyperbolic metric space, without any further assumptions, possesses a slim $(n+1)$-simplex property analogous to the slimness of quasi-geodesic triangles in Gromov hyperbolic spaces. In connection with"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.08153","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2206.08153/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}