# Combinatorial and metric properties of Thompson's group T

@article{Burillo2005CombinatorialAM, title={Combinatorial and metric properties of Thompson's group T}, author={J. Burillo and S. Cleary and M. Stein and J. Taback}, journal={Transactions of the American Mathematical Society}, year={2005}, volume={361}, pages={631-652} }

We discuss metric and combinatorial properties of Thompson's group T, such as the normal forms for elements and uniqueness of tree pair diagrams. We relate these properties to those of Thompson's group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements into convenient pieces. We show that the number of carets in a reduced representative of T estimates the word… Expand

#### 38 Citations

The automorphism group of Thompson's group F: subgroups and metric properties.

- Mathematics
- 2011

We describe some of the geometric properties of the automorphism group Aut(F) of Thompson's group F. We give realizations of Aut(F) geometrically via periodic tree pair diagrams, which lead to… Expand

An Irrational-slope Thompson's Group

- Mathematics
- 2018

The purpose of this paper is to study the properties of the irrational-slope Thompson's group $F_\tau$ introduced by Cleary in 1995. We construct presentations, both finite and infinite and we… Expand

METRIC PROPERTIES OF HIGHER-DIMENSIONAL THOMPSON'S GROUPS

- Mathematics
- 2008

Higher-dimensional Thompson's groups nV are finitely presented groups that generalize dyadic self-maps of the unit interval to dyadic self-maps of n-dimensional unit cubes. We describe some of the… Expand

Thompson’s Group T, Undistorted Free Groups and Automorphisms of the Flip Graph

- Mathematics
- 2014

In this paper we present combinatorial and geometric results about Thompson’s group T by comparing multiple viewpoints of the same object and their interactions (see [3] for an introduction to… Expand

Metric properties of the braided Thompson's groups

- Mathematics
- 2007

Braided Thompson's groups are finitely presented groups introduced by Brin and Dehornoy which contain the ordinary braid groups $B_n$, the finitary braid group $B_{\infty}$ and Thompson's group $F$… Expand

Conjugacy in Thompson's Groups

- Mathematics
- 2007

We give a unified solution the conjugacy problem in Thompson’s groups F , V , and T using strand diagrams, a modification of tree diagrams. We then analyze the complexity of the resulting algorithms.… Expand

PSL(2,Z) as a non distorted subgroup of Thompson's group T

- Mathematics
- 2010

In this paper we characterize the elements of PSL(2,Z), as a subgroup of Thompson group T, in the language of reduced tree pair diagrams and in terms of piecewise linear maps as well. Actually, we… Expand

Note on the number of conjugacy classes of torsion elements on Thompson ’ s group

- 2013

We prove that there are exactly φ(n) conjugacy classes of elements of order n on Thompson group T , where φ is the Euler function. We also give a representation of elements of T in terms of… Expand

Pure braid subgroups of braided Thompson's groups

- Mathematics
- 2006

We describe some properties of braided generalizations of Thompson's groups, introduced by Brin and Dehornoy. We give slightly different characterizations of the braided Thompson's groups $BV$ and… Expand

On the number of conjugacy classes of torsion elements on Thompson ’ s group T Ariadna Fossas

- 2012

We prove that there are exactly φ(n) conjugacy classes of elements of order n on Thompson group T , where φ is the Euler function. We also give a representation of elements of T in terms of… Expand

#### References

SHOWING 1-10 OF 25 REFERENCES

Combinatorial properties of Thompson's group F

- Mathematics
- 2002

We study some combinatorial consequences of Blake Fordham's theorems on the word metric of Thompson's group F in the standard two generator presentation. We explore connections between the tree pair… Expand

Metrics and embeddings of generalizations of Thompson’s group $F$

- Mathematics
- 1998

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… Expand

Forest Diagrams for Elements of Thompson's Group F

- Mathematics, Computer Science
- Int. J. Algebra Comput.
- 2005

We introduce forest diagrams to represent elements of Thompson's group F. These diagrams relate to a certain action of F on the real line in the same way that tree diagrams relate to the standard… Expand

Minimal Length Elements of Thompson's Group F

- Mathematics
- 2003

Elements of the group are represented by pairs of binary trees and the structure of the trees gives insight into the properties of the elements of the group. The review section presents this… Expand

On the Properties of The Cayley Graph of Richard Thompson's Group F

- Mathematics, Computer Science
- Int. J. Algebra Comput.
- 2004

The growth rate of F, R. Thompson's group F in generators x0, x1, has a lower bound of . Expand

Quasi-Isometrically Embedded Subgroups of Thompson's GroupF

- Mathematics
- 1998

Abstract The goal of this paper is to study subgroups of Thompson's group F which are isomorphic to F × Z n and F × F . A result estimating the norm of an element of Thompson's group is found,… Expand

Sur un groupe remarquable de difféomorphismes du cercle

- Mathematics
- 1987

The Göttingen State and University Library provides access to digitized documents strictly for noncommercial educational, research and private purposes and makes no warranty with regard to their use… Expand

Introductory notes on Richard Thompson’s groups, Enseign

- 1996

An infinite-dimensional torsion-free FP∞

- group, Inventiones Mathematicae
- 1984

Brown , Forest diagrams for elements of Thompson ’ s group F , Internat

- J . Algebra Comput .
- 2005