An Irrational-slope Thompson's Group. / Burillo, José; Nucinkis, Brita; Reeves, Lawrence.

In: Publicacions Matemàtiques , 01.09.2020.

Research output: Contribution to journalArticlepeer-review

Forthcoming

### Standard

An Irrational-slope Thompson's Group. / Burillo, José; Nucinkis, Brita; Reeves, Lawrence.

In: Publicacions Matemàtiques , 01.09.2020.

Research output: Contribution to journalArticlepeer-review

### Harvard

Burillo, J, Nucinkis, B & Reeves, L 2020, 'An Irrational-slope Thompson's Group', Publicacions Matemàtiques . <https://arxiv.org/abs/1806.00108v3>

### APA

Burillo, J., Nucinkis, B., & Reeves, L. (Accepted/In press). An Irrational-slope Thompson's Group. Publicacions Matemàtiques . https://arxiv.org/abs/1806.00108v3

### Vancouver

Burillo J, Nucinkis B, Reeves L. An Irrational-slope Thompson's Group. Publicacions Matemàtiques . 2020 Sep 1.

### Author

Burillo, José ; Nucinkis, Brita ; Reeves, Lawrence. / An Irrational-slope Thompson's Group. In: Publicacions Matemàtiques . 2020.

### BibTeX

@article{a51acbc40d894e459d68983a065ca33d,
title = "An Irrational-slope Thompson's Group",
abstract = "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 describe its combinatorial structure using binary trees. We show that its commutator group is simple. Finally, inspired by the case of Thompson's group F, we define a unique normal form for the elements of the group and study the metric properties for the elements based on this normal form. As a corollary, we see that several embeddings of $F$ in $F_\tau$ are undistorted. ",
keywords = "math.GR, 20F65",
author = "Jos{\'e} Burillo and Brita Nucinkis and Lawrence Reeves",
note = "30 pages, 18 figures",
year = "2020",
month = sep,
day = "1",
language = "English",
journal = "Publicacions Matem{\`a}tiques ",
issn = "2014-4350",

}

### RIS

TY - JOUR

T1 - An Irrational-slope Thompson's Group

AU - Burillo, José

AU - Nucinkis, Brita

AU - Reeves, Lawrence

N1 - 30 pages, 18 figures

PY - 2020/9/1

Y1 - 2020/9/1

N2 - 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 describe its combinatorial structure using binary trees. We show that its commutator group is simple. Finally, inspired by the case of Thompson's group F, we define a unique normal form for the elements of the group and study the metric properties for the elements based on this normal form. As a corollary, we see that several embeddings of $F$ in $F_\tau$ are undistorted.

AB - 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 describe its combinatorial structure using binary trees. We show that its commutator group is simple. Finally, inspired by the case of Thompson's group F, we define a unique normal form for the elements of the group and study the metric properties for the elements based on this normal form. As a corollary, we see that several embeddings of $F$ in $F_\tau$ are undistorted.

KW - math.GR

KW - 20F65

M3 - Article

JO - Publicacions Matemàtiques

JF - Publicacions Matemàtiques

SN - 2014-4350

ER -