{"paper":{"title":"On geodesic ray bundles in buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"Timoth\\'ee Marquis","submitted_at":"2017-08-28T17:30:53Z","abstract_excerpt":"Let $X$ be a building, identified with its Davis realisation. In this paper, we provide for each $x\\in X$ and each $\\eta$ in the visual boundary $\\partial X$ of $X$ a description of the geodesic ray bundle $Geo(x,\\eta)$, namely, of the reunion of all combinatorial geodesic rays (corresponding to infinite minimal galleries in the chamber graph of $X$) starting from $x$ and pointing towards $\\eta$. When $X$ is locally finite and hyperbolic, we show that the symmetric difference between $Geo(x,\\eta)$ and $Geo(y,\\eta)$ is always finite, for $x,y\\in X$ and $\\eta\\in\\partial X$. This gives a positive"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1708.08431","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":""},"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"}