Cylinders, multi-cylinders and the induced action of $Aut(F_n)$
Group Theory
2012-11-13 v1
Abstract
A cylinder is the set of infinite words with fixed prefix . A double-cylinder is "the same" for bi-infinite words. We show that for every word and any automorphism of the free group the image is a finite union of cylinders. The analogous statement is true for double cylinders. We give (a) an algorithm, and (b) a precise formula which allows one to determine this finite union of cylinders.
Keywords
Cite
@article{arxiv.1211.2347,
title = {Cylinders, multi-cylinders and the induced action of $Aut(F_n)$},
author = {Fedaa Ibrahim},
journal= {arXiv preprint arXiv:1211.2347},
year = {2012}
}