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arxiv: 1311.3880 · v2 · pith:WPSCQVTLnew · submitted 2013-11-15 · 🧮 math.DS · math.FA· math.OA

Groupoid Actions on Fractafolds

classification 🧮 math.DS math.FAmath.OA
keywords groupoidbundleactionrenault-deaconuactionsalgebraassociatedblowup
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We define a bundle over a totally disconnected set such that each fiber is homeomorphic to a fractal blowup. We prove that there is a natural action of a Renault-Deaconu groupoid on our fractafold bundle and that the resulting action groupoid is a Renault-Deaconu groupoid itself. We also show that when the bundle is locally compact the associated $C^*$-algebra is primitive and has a densely defined lower-semicontinuous trace.

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