Automata, groups, limit spaces, and tilings

[摘要] 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. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2006-11-15

[关键词] automata;groups;tilings;self-coverings;solenoids;tree automorphisms