{"paper":{"title":"Group actions on multitrees and the $K$-theory of their crossed products","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.GR","math.KT"],"primary_cat":"math.OA","authors_text":"Anne Thomas, Jack Spielberg, Nathan Brownlowe, Victor Wu","submitted_at":"2023-11-09T11:29:27Z","abstract_excerpt":"We study group actions on multitrees, which are directed graphs in which there is at most one directed path between any two vertices. In our main result we describe a six-term exact sequence in $K$-theory for the reduced crossed product $C_0(\\partial E)\\rtimes_r G$ induced from the action of a countable discrete group $G$ on a row-finite, finitely-aligned multitree $E$ with no sources. We provide formulas for the $K$-theory of $C_0(\\partial E) \\rtimes_r G$ in the case where $G$ acts freely on $E$, and in the case where all vertex stabilisers are infinite cyclic. We study the action $G\\curvearr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2311.05285","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2311.05285/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}