Automata, Groups, Limit Spaces, and Tilings
Group Theory
2009-11-27 v2
Abstract
We explore the connections between automata, groups, limit spaces of self-similar actions, and tilings. In particular, we show how a group acting ``nicely'' on a tree gives rise to a self-covering of a topological groupoid, and how the group can be reconstructed from the groupoid and its covering. The connection is via finite-state automata. These define decomposition rules, or self-similar tilings, on leaves of the solenoid associated with the covering.
Cite
@article{arxiv.math/0412373,
title = {Automata, Groups, Limit Spaces, and Tilings},
author = {Laurent Bartholdi and Andre G. Henriques and Volodymyr V. Nekrashevych},
journal= {arXiv preprint arXiv:math/0412373},
year = {2009}
}
Comments
to appear in J. Algebra