Metrics and embeddings of generalizations of Thompson's group F

Jose Burillo; Sean Cleary; Melanie Stein

Metrics and embeddings of generalizations of Thompson's group F

Group Theory 2018-03-28 v3 Geometric Topology

Authors: Jose Burillo , Sean Cleary , Melanie Stein

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.

Keywords

thompson's group f generalizations f(p) word metric quasi-isometric embedding reduced rooted tree diagrams shift maps

Cite

@article{arxiv.math/9809185,
  title  = {Metrics and embeddings of generalizations of Thompson's group F},
  author = {Jose Burillo and Sean Cleary and Melanie Stein},
  journal= {arXiv preprint arXiv:math/9809185},
  year   = {2018}
}

Comments

16 pages, with figures created using pictex.tex under AMS-TeX, updated with more embeddings of F(p) into F(q)

Metrics and embeddings of generalizations of Thompson's group F

Abstract

Keywords

Cite

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