{"paper":{"title":"Invariant boundary distributions for finite graphs","license":"","headline":"","cross_cats":["math.OA"],"primary_cat":"math.GR","authors_text":"Guyan Robertson","submitted_at":"2008-01-04T12:00:41Z","abstract_excerpt":"Let $\\Gamma$ be the fundamental group of a finite connected graph $\\mathcal G$. Let $\\mathfrak M$ be an abelian group. A {\\it distribution} on the boundary $\\partial\\Delta$ of the universal covering tree $\\Delta$ is an $\\mathfrak M$-valued measure defined on clopen sets. If $\\mathfrak M$ has no $\\chi(\\mathcal G)$-torsion then the group of $\\Gamma$-invariant distributions on $\\partial\\Delta$ is isomorphic to $H_1(\\mathcal G,\\mathfrak M)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0801.0667","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"}