Locally free actions of groupoids and proper topological correspondences

2017/09/26 by Rohit Dilip Holkar, Holkar, Rohit Dilip
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #math.OA

paper · pdf · doi:10.48550/arxiv.1709.08938

43 pages, 3 figures. Comments are welcome

arxiv created 2017/09/26 · arxiv updated 2017/09/27

Abstract

Let (G,α) and (H,β) be locally compact Hausdorff groupoids with Haar systems, and let (X,λ) be a topological correspondence from (G,α) to (H,β) which induce the C^*-correspondence H(X)\colon C^*(G,α)→ C^*(H,β). We give sufficient topological conditions which when satisfied the C^*-correspondence H(X) is proper, that is, the C^*-algebra C^*(G,α) acts on the Hilbert C^*(H,β)-module H(X) via the comapct operators. Thus a proper topological correspondence produces an element in KK(C^*(G,α),C^*(H,β)).

Related

• Topological construction of C^*-correspondences for groupoid C^*-algebras
• Composition of topological correspondences
• The bicategory of topological correspondences
• Non-Hausdorff groupoids, proper actions and K-theory
• Morphisms of locally compact groupoids endowed with Haar systems