Rearrangement groups of fractals
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- by James Belk and Bradley Forrest PDF
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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
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Additional Information
- James Belk
- Affiliation: Mathematical Institute, University of St Andrews, St Andrews KY16 9AJ, United Kingdom
- MR Author ID: 760112
- Bradley Forrest
- Affiliation: School of Natural Sciences and Mathematics, Richard Stockton College of New Jersey, P. O. Box 195, Pomona, New Jersey 08240
- MR Author ID: 834589
- Received by editor(s): July 25, 2016
- Received by editor(s) in revised form: June 3, 2017
- Published electronically: July 2, 2019
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 4509-4552
- MSC (2010): Primary 20F65; Secondary 20F38, 28A80
- DOI: https://doi.org/10.1090/tran/7386
- MathSciNet review: 4009393