{"paper":{"title":"What is a horocyclic product, and how is it related to lamplighters?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.MG"],"primary_cat":"math.GR","authors_text":"Wolfgang Woess","submitted_at":"2014-01-09T12:19:44Z","abstract_excerpt":"This is a rather personal introductory outline of an interesting class of geometric, resp. graph- and group-theoretical structures. After an introductive section about their genesis, the general construction of horocyclic products is presented. Three closely related basic structures of this type are explained in more detail: Diestel-Leader graphs, treebolic spaces, and Sol-groups, resp. -manifolds. Emphasis is on their geometry, isometry groups, quasi-isometry classification and boundary at infinity. Subsequently, it is clarified under which parametrisation they admit discrete groups of isomet"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1976","kind":"arxiv","version":1},"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"}