UNIGE document Scientific Article
previous document  unige:11945  next document
add to browser collection
Title

Schreier graphs of the Basilica group

Authors
D'Angeli, Daniele
Nagnibeda, Tatiana
Published in Journal of Modern Dynamics. 2010, vol. 4, no. 1, p. 139-177
Abstract With any self-similar action of a finitely generated group $G$ of automorphisms of a regular rooted tree $T$ can be naturally associated an infinite sequence of finite graphs ${Gamma_n}_{ngeq 1}$, where $Gamma_n$ is the Schreier graph of the action of $G$ on the $n$-th level of $T$. Moreover, the action of $G$ on $partial T$ gives rise to orbital Schreier graphs $Gamma_{xi}$, $xiin partial T$. Denoting by $xi_n$ the prefix of length $n$ of the infinite ray $xi$, the rooted graph $(Gamma_{xi},xi)$ is then the limit of the sequence of finite rooted graphs ${(Gamma_n,xi_n)}_{ngeq 1}$ in the sense of pointed Gromov-Hausdorff convergence. In this paper, we give a complete classification (up to isomorphism) of the limit graphs $(Gamma_{xi},xi)$ associated with the Basilica group acting on the binary tree, in terms of the infinite binary sequence $xi$.
Identifiers
Full text
Article (618 Kb) - public document Free access
Structures
Citation
(ISO format)
D'ANGELI, Daniele et al. Schreier graphs of the Basilica group. In: Journal of Modern Dynamics, 2010, vol. 4, n° 1, p. 139-177. https://archive-ouverte.unige.ch/unige:11945

214 hits

81 downloads

Update

Deposited on : 2010-09-28

Export document
Format :
Citation style :