{"paper":{"title":"Locally free actions of groupoids and proper topological correspondences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Rohit Dilip Holkar","submitted_at":"2017-09-26T10:55:57Z","abstract_excerpt":"Let $(G,\\alpha)$ and $(H,\\beta)$ be locally compact Hausdorff groupoids with Haar systems, and let $(X,\\lambda)$ be a topological correspondence from $(G,\\alpha)$ to $(H,\\beta)$ which induce the ${C}^*$-correspondence $\\mathcal{H}(X)\\colon {C}^*(G,\\alpha)\\to {C}^*(H,\\beta)$. We give sufficient topological conditions which when satisfied the ${C}^*$-correspondence $\\mathcal{H}(X)$ is proper, that is, the ${C}^*$-algebra ${C}^*(G,\\alpha)$ acts on the Hilbert ${C}^*(H,\\beta)$-module ${H}(X)$ via the comapct operators. Thus a proper topological correspondence produces an element in ${KK}({C}^*(G,\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.08938","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"}