%0 Journal Article
%T Sturmian morphisms, the braid group B_4, Christoffel words and bases of F_2
%A Christian Kassel
%A Christophe Reutenauer
%J Mathematics
%D 2005
%I arXiv
%R 10.1007/s10231-006-0008-z
%X We give a presentation by generators and relations of a certain monoid generating a subgroup of index two in the group Aut(F_2) of automorphisms of the rank two free group F_2 and show that it can be realized as a monoid in the group B_4 of braids on four strings. In the second part we use Christoffel words to construct an explicit basis of F_2 lifting any given basis of the free abelian group Z^2. We further give an algorithm allowing to decide whether two elements of F_2 form a basis or not. We also show that, under suitable conditions, a basis has a unique conjugate consisting of two palindromes.
%U http://arxiv.org/abs/math/0507219v1