{"paper":{"title":"$K$-theory and homotopies of 2-cocycles on transformation groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.OA","authors_text":"Elizabeth Gillaspy","submitted_at":"2014-02-13T20:46:16Z","abstract_excerpt":"This paper constitutes a first step in the author's program to investigate the question of when a homotopy of 2-cocycles $\\omega = \\{\\omega_t\\}_{t \\in [0,1]}$ on a locally compact Hausdorff groupoid $\\mathcal{G}$ induces an isomorphism of the $K$-theory groups of the reduced twisted groupoid $C^*$-algebras: $K_*(C^*_r(\\mathcal{G}, \\omega_0)) \\cong K_*(C^*_r(\\mathcal{G}, \\omega_1)).$ Generalizing work of Echterhoff, L\\\"uck, Phillips, and Walters from 2010, we show that if $\\mathcal{G} = G \\ltimes X$ is a second countable locally compact transformation group, then whenever $G$ satisfies the Baum"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.3280","kind":"arxiv","version":3},"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"}