Groupoid Actions on Fractafolds
Dynamical Systems
2014-07-01 v2 Functional Analysis
Operator Algebras
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 -algebra is primitive and has a densely defined lower-semicontinuous trace.
Keywords
Cite
@article{arxiv.1311.3880,
title = {Groupoid Actions on Fractafolds},
author = {Marius Ionescu and Alex Kumjian},
journal= {arXiv preprint arXiv:1311.3880},
year = {2014}
}
Comments
SIGMA 10 (2014), 068, 14 pages