Fell bundles and imprimitivity theorems: Mansfield's and Fell's theorems
S. Kaliszewski, Paul S. Muhly, John Quigg, Dana P. Williams
TL;DR
This paper uses Fell bundles over groupoids to recover and relate Mansfield's and Fell's imprimitivity theorems, providing new insights and automatic amenability results for transformation Fell bundles.
Contribution
It introduces a unified approach to imprimitivity theorems using Fell bundles over groupoids and connects different versions through Rieffel Surjection, also establishing automatic amenability.
Findings
Unified framework for Mansfield's and Fell's theorems
Relation between different versions via Rieffel Surjection
Automatic amenability results for certain Fell bundles
Abstract
In the third and latest paper in this series, we recover the imprimitivity theorems of Mansfield and Fell using our technique of Fell bundles over groupoids. Also, we apply the Rieffel Surjection of the first paper in the series to relate our version of Mansfield's theorem to that of an Huef and Raeburn, and to give an automatic amenability result for certain transformation Fell bundles.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Advanced Operator Algebra Research