English

Cylinders, multi-cylinders and the induced action of $Aut(F_n)$

Group Theory 2012-11-13 v1

Abstract

A cylinder Cu1C^1_u is the set of infinite words with fixed prefix uu. A double-cylinder C[1,u]2C^2_{[1,u]} is "the same" for bi-infinite words. We show that for every word uu and any automorphism φ\varphi of the free group FF the image φ(Cu1)\varphi(C^1_u) 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}
}