Centralizers in the R. Thompson group Vn

Collin Bleak; Hannah Bowman; Alison G Lynch; Garret Graham; Jacob Hughes; Francesco Matucci; Eugenia Sapir

Centralizers in the R. Thompson group Vn

Collin Bleak, Hannah Bowman, Alison G Lynch, Garret Graham, Jacob Hughes, Francesco Matucci, Eugenia Sapir

Department of Mathematics and Statistics

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

Abstract

Let n ≥ 2 and let α ∈ Vn be an element in the Higman-Thompson group Vn. We study the structure of the centralizer of α ∈ Vn through a careful analysis of the action of hαi on the Cantor set C. We make use of revealing tree pairs as developed by Brin and Salazar from which we derive discrete train tracks and flow graphs to assist us in our analysis. A consequence of our structure theorem is that element centralizers are finitely generated. Along the way we give a short argument using revealing tree pairs which shows that cyclic groups are undistorted in Vn.

Original language	American English
Journal	Groups, Geometry, and Dynamics
Volume	7
State	Published - 2013

Disciplines

Mathematics

Cite this

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title = "Centralizers in the R. Thompson group Vn",

abstract = " Let n ≥ 2 and let α ∈ Vn be an element in the Higman-Thompson group Vn. We study the structure of the centralizer of α ∈ Vn through a careful analysis of the action of hαi on the Cantor set C. We make use of revealing tree pairs as developed by Brin and Salazar from which we derive discrete train tracks and flow graphs to assist us in our analysis. A consequence of our structure theorem is that element centralizers are finitely generated. Along the way we give a short argument using revealing tree pairs which shows that cyclic groups are undistorted in Vn.",

author = "Collin Bleak and Hannah Bowman and Lynch, {Alison G} and Garret Graham and Jacob Hughes and Francesco Matucci and Eugenia Sapir",

year = "2013",

language = "American English",

volume = "7",

journal = "Groups, Geometry, and Dynamics",

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TY - JOUR

T1 - Centralizers in the R. Thompson group Vn

AU - Bleak, Collin

AU - Bowman, Hannah

AU - Lynch, Alison G

AU - Graham, Garret

AU - Hughes, Jacob

AU - Matucci, Francesco

AU - Sapir, Eugenia

PY - 2013

Y1 - 2013

N2 - Let n ≥ 2 and let α ∈ Vn be an element in the Higman-Thompson group Vn. We study the structure of the centralizer of α ∈ Vn through a careful analysis of the action of hαi on the Cantor set C. We make use of revealing tree pairs as developed by Brin and Salazar from which we derive discrete train tracks and flow graphs to assist us in our analysis. A consequence of our structure theorem is that element centralizers are finitely generated. Along the way we give a short argument using revealing tree pairs which shows that cyclic groups are undistorted in Vn.

AB - Let n ≥ 2 and let α ∈ Vn be an element in the Higman-Thompson group Vn. We study the structure of the centralizer of α ∈ Vn through a careful analysis of the action of hαi on the Cantor set C. We make use of revealing tree pairs as developed by Brin and Salazar from which we derive discrete train tracks and flow graphs to assist us in our analysis. A consequence of our structure theorem is that element centralizers are finitely generated. Along the way we give a short argument using revealing tree pairs which shows that cyclic groups are undistorted in Vn.

UR - https://arxiv.org/pdf/1107.0672.pdf

M3 - Article

VL - 7

JO - Groups, Geometry, and Dynamics

JF - Groups, Geometry, and Dynamics

ER -

Centralizers in the R. Thompson group Vn

Abstract

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