{"paper":{"title":"A Local-to-Global Result for Topological Spherical Buildings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.MG","authors_text":"Rupert McCallum","submitted_at":"2010-09-22T02:25:03Z","abstract_excerpt":"Suppose that \\Delta, \\Delta' are two buildings each arising from a semisimpe algebraic group over a field, a topological field in the former case, and that for both the buildings the Coxeter diagram has no isolated nodes. We give conditions under which a partially defined injective chamber map, whose domain is the subcomplex of \\Delta, generated by a nonempty open set of chambers, and whose codomain is \\Delta', is guaranteed to extend to a unique injective chamber map. Related to this result is a local version of the Borel-Tits theorem on abstract homomorphisms of simple algebraic groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.4249","kind":"arxiv","version":12},"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"}