This article is cited in 2 papers

Groupoid Actions on Fractafolds

Marius Ionescu^a, Alex Kumjian<sup>b

a</sup> Department of Mathematics, United States Naval Academy, Annapolis, MD, 21402-5002, USA
^b Department of Mathematics, University of Nevada, Reno, NV, 89557, USA

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.

Keywords: Renault–Deaconu groupoids; fractafolds; iterated function systems.

MSC: 28A80; 22A22; 46L55; 46L05

Received: February 4, 2014; in final form June 21, 2014; Published online June 28, 2014

Language: English

DOI: 10.3842/SIGMA.2014.068

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ArXiv: 1311.3880