Infinite words and universal free actions

Abstract

This is the second paper in a series of three, where we take on the unified theory of non-Archimedean group actions, length functions and infinite words. Here, for an arbitrary group $G$ of infinite words over an ordered abelian group $\Lambda$ we construct a $\Lambda$-tree ${\Gamma }_G$ equipped with a free action of $G$. Moreover, we show that ${\Gamma }_G$ is a universal tree for $G$ in the sense that it isometrically embeds in every $\Lambda$-tree equipped with a free $G$-action compatible with the original length function on $G$.

20 pages, 4 figures

References in corpus (3)

• Limit groups and groups acting freely on R^n-trees
• Finite index subgroups of fully residually free groups
• Groups with free regular length functions in Z^n

Cited by in corpus (4)

• Membership Problem in groups acting freely on Z^n-trees
• Affine actions on non-archimedean trees
• Groups acting on hyperbolic $\Lambda$-metric spaces
• Regular completions of ${\mathbb{Z}}^n$-free groups