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

Research output: Contribution to journal › Article › peer-review

Forthcoming

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

Research output: Contribution to journal › Article › peer-review

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

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

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

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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",

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journal = "Publicacions Matem{\`a}tiques ",

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AU - Nucinkis, Brita

AU - Reeves, Lawrence

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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

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