{"paper":{"title":"$K$-theory and homotopies of 2-cocycles on higher-rank graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Elizabeth Gillaspy","submitted_at":"2014-03-15T13:07:54Z","abstract_excerpt":"This paper continues our investigation into the question of when a homotopy $\\omega = \\{\\omega_t\\}_{t \\in [0,1]}$ of 2-cocycles on a locally compact Hausdorff groupoid $\\mathcal{G}$ gives rise to an isomorphism of the $K$-theory groups of the twisted groupoid $C^*$-algebras: $K_*(C^*(\\mathcal{G}, \\omega_0)) \\cong K_*(C^*(\\mathcal{G}, \\omega_1)).$ In particular, we build on work by Kumjian, Pask, and Sims to show that if $\\mathcal{G} = \\mathcal{G}_\\Lambda$ is the infinite path groupoid associated to a row-finite higher-rank graph $\\Lambda$ with no sources, and $\\{c_t\\}_{t \\in [0,1]}$ is a homot"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.3799","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"}