Groupoid Actions on Fractafolds
classification
🧮 math.DS
math.FAmath.OA
keywords
groupoidbundleactionrenault-deaconuactionsalgebraassociatedblowup
read the original abstract
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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