{"paper":{"title":"Connectivity Properties for Actions on Locally Finite Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Keith Jones","submitted_at":"2011-11-03T15:11:52Z","abstract_excerpt":"Given an action by a finitely generated group G on a locally finite tree T, we view points of the visual boundary \\partialT as directions in T and use {\\rho} to lift this sense of direction to G. For each point E \\in \\partialT, this allows us to ask if G is (n - 1)-connected \"in the direction of E\". The invariant {\\Sigma}^n({\\rho}) \\subseteq \\partialT then records the set of directions in which G is (n-1)-connected. In this paper, we introduce a family of actions for which {\\Sigma}^1({\\rho}) can be calculated through analysis of certain quotient maps between trees. We show that for actions of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.0871","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"}