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Metrics and embeddings of generalizations of Thompson's group F

Jose Burillo·Sean Cleary·Melanie Stein
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Abstract

The distance from the origin in the word metric for generalizations F(p) of Thompson's group F is quasi-isometric to the number of carets in the reduced rooted tree diagrams representing the elements of F(p). This interpretation of the metric is used to prove that every F(p) admits a quasi-isometric embedding into every F(q), and also to study the behavior of the shift maps under these embeddings.

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Jose Burillo, Sean Cleary, Melanie Stein. 1998-12-14. Metrics and embeddings of generalizations of Thompson's group F. https://arxiv.org/abs/math/9809185

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