A palindromization map for the free group
Combinatorics
2010-03-25 v2 Group Theory
Abstract
We define a self-map Pal: F_2 --> F_2 of the free group on two generators a, b, using automorphisms of F_2 that form a group isomorphic to the braid group B_3. The map Pal restricts to de Luca's right iterated palindromic closure on the submonoid generated by a, b, and is continuous for the profinite topology on F_2. The values of Pal are palindromes and coincide with the elements g of F_2 such that abg is conjugate to bag.
Keywords
Cite
@article{arxiv.0802.4359,
title = {A palindromization map for the free group},
author = {Christian Kassel and Christophe Reutenauer},
journal= {arXiv preprint arXiv:0802.4359},
year = {2010}
}
Comments
14 pages. Introduction expanded. Two references added. Sections 3 and 6 of Version 1 have been restructured, now forming Sections 3-4