Conjugacy and dynamics in almost automorphism groups of trees

Gil Goffer; Waltraud Lederle

doi:10.1142/S0218196721500557

Conjugacy and dynamics in almost automorphism groups of trees

Gil Goffer, Waltraud Lederle

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

Abstract

We determine when two almost automorphisms of a regular tree are conjugate. This is done by combining the classification of conjugacy classes in the automorphism group of a level-homogeneous tree by Gawron, Nekrashevych and Sushchansky and the solution of the conjugacy problem in Thompson’s V by Belk and Matucci. We also analyze the dynamics of a tree almost automorphism as a homeomorphism of the boundary of the tree.

Original language	English
Pages (from-to)	1497-1545
Number of pages	49
Journal	International Journal of Algebra and Computation
Volume	31
Issue number	8
DOIs	https://doi.org/10.1142/S0218196721500557
State	Published - 1 Dec 2021
Externally published	Yes

Keywords

Conjugacy
Neretin’s group
orbital types
strand diagrams
tree almost automorphisms

ASJC Scopus subject areas

General Mathematics

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10.1142/S0218196721500557

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AU - Lederle, Waltraud

PY - 2021/12/1

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N2 - We determine when two almost automorphisms of a regular tree are conjugate. This is done by combining the classification of conjugacy classes in the automorphism group of a level-homogeneous tree by Gawron, Nekrashevych and Sushchansky and the solution of the conjugacy problem in Thompson’s V by Belk and Matucci. We also analyze the dynamics of a tree almost automorphism as a homeomorphism of the boundary of the tree.

AB - We determine when two almost automorphisms of a regular tree are conjugate. This is done by combining the classification of conjugacy classes in the automorphism group of a level-homogeneous tree by Gawron, Nekrashevych and Sushchansky and the solution of the conjugacy problem in Thompson’s V by Belk and Matucci. We also analyze the dynamics of a tree almost automorphism as a homeomorphism of the boundary of the tree.

KW - Conjugacy

KW - Neretin’s group

KW - orbital types

KW - strand diagrams

KW - tree almost automorphisms

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U2 - 10.1142/S0218196721500557

DO - 10.1142/S0218196721500557

M3 - Article

AN - SCOPUS:85114103392

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JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 8

ER -

Conjugacy and dynamics in almost automorphism groups of trees

Abstract

Keywords

ASJC Scopus subject areas

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