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Quasi-isometrically embedded subgroups of Thompson's group F

Jose Burillo
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Abstract

The goal of this paper is to construct quasi-isometrically embedded subgroups of Thompson's group $F$ which are isomorphic to $\fz^n$ for all $n$. A result estimating the norm of an element of Thompson's group is found. As a corollary, Thompson's group is seen to be an example of a finitely presented group which has an infinite-dimensional asymptotic cone.

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Jose Burillo. 1998-02-19. Quasi-isometrically embedded subgroups of Thompson's group F. https://arxiv.org/abs/math/9802095

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