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arXiv · 1107.0425

Infinite words and universal free actions

Olga Kharlampovich·Alexei Myasnikov·Denis Serbin
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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 $G$.

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Olga Kharlampovich, Alexei Myasnikov, Denis Serbin. 2011-07-03. Infinite words and universal free actions. https://doi.org/10.1515/gcc-2014-0005

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