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• W2598862757 abstract "Abstract We extend Matui’s notion of almost finiteness to general étale groupoids and show that the reduced groupoid C$^{ast }$-algebras of minimal almost finite groupoids have stable rank 1. The proof follows a new strategy, which can be regarded as a local version of the large subalgebra argument. The following three are the main consequences of our result: (1) for any group of (local) subexponential growth and for any its minimal action admitting a totally disconnected free factor, the crossed product has stable rank 1; (2) any countable amenable group admits a minimal action on the Cantor set, all whose minimal extensions form the crossed product of stable rank 1; and (3) for any amenable group, the crossed product of the universal minimal action has stable rank 1." @default.
• W2598862757 created "2017-04-07" @default.
• W2598862757 creator A5045896292 @default.
• W2598862757 date "2018-08-14" @default.
• W2598862757 modified "2023-10-18" @default.
• W2598862757 title "Almost Finiteness for General Étale Groupoids and Its Applications to Stable Rank of Crossed Products" @default.
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• W2598862757 doi "https://doi.org/10.1093/imrn/rny187" @default.
• W2598862757 hasPublicationYear "2018" @default.
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