Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Rearrangement groups of fractals


Authors: James Belk and Bradley Forrest
Journal: Trans. Amer. Math. Soc. 372 (2019), 4509-4552
MSC (2010): Primary 20F65; Secondary 20F38, 28A80
DOI: https://doi.org/10.1090/tran/7386
Published electronically: July 2, 2019
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We construct rearrangement groups for edge replacement systems, an infinite class of groups that generalize Richard Thompson's groups $ F$, $ T$, and $ V$. Rearrangement groups act by piecewise-defined homeomorphisms on many self-similar topological spaces, among them the Vicsek fractal and many Julia sets. We show that every rearrangement group acts properly on a locally finite $ \mathrm {CAT}(0)$ cubical complex, and we use this action to prove that certain rearrangement groups are of type $ F_{\infty }$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 20F65, 20F38, 28A80

Retrieve articles in all journals with MSC (2010): 20F65, 20F38, 28A80


Additional Information

James Belk
Affiliation: Mathematical Institute, University of St Andrews, St Andrews KY16 9AJ, United Kingdom

Bradley Forrest
Affiliation: School of Natural Sciences and Mathematics, Richard Stockton College of New Jersey, P. O. Box 195, Pomona, New Jersey 08240

DOI: https://doi.org/10.1090/tran/7386
Received by editor(s): July 25, 2016
Received by editor(s) in revised form: June 3, 2017
Published electronically: July 2, 2019
Article copyright: © Copyright 2019 American Mathematical Society