{"paper":{"title":"Visual boundaries of Diestel-Leader graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Gregory A. Kelsey, Keith Jones","submitted_at":"2013-07-08T16:59:18Z","abstract_excerpt":"Diestel-Leader graphs are neither hyperbolic nor CAT(0), so their visual boundaries may be pathological. Indeed, we show that for $d>2$, $\\partial\\text{DL}_d(q)$ carries the indiscrete topology. On the other hand, $\\partial\\text{DL}_2(q)$, while not Hausdorff, is $T_1$, totally disconnected, and compact. Since $\\text{DL}_2(q)$ is a Cayley graph of the lamplighter group $L_q$, we also obtain a nice description of $\\partial\\text{DL}_2(q)$ in terms of the lamp stand model of $L_q$ and discuss the dynamics of the action."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.2163","kind":"arxiv","version":2},"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"}