Groupoid Actions on Fractafolds - Ionescu, M.; Kumjian, A. (Symmetry, Integrability and Geometry: Methods and Applications, 2014)
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.