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Quasi-automorphisms of the infinite rooted 2-edge-coloured binary tree

Quasi-automorphisms of the infinite rooted 2-edge-coloured binary tree
Quasi-automorphisms of the infinite rooted 2-edge-coloured binary tree

We study the groupQV , the self-maps of the infinite 2-edge coloured binary tree which preserve the edge and colour relations at cofinitely many locations. We introduce related groups QF , QT , zQ T , and zQV , prove that QF , zQ T , and zQV are of type F1, and calculate finite presentations for them. We calculate the normal subgroup structure of all 5 groups, the Bieri-Neumann-Strebel-Renz invariants of QF , and discuss the relationship of all 5 groups with other generalisations of Thompson's groups.

Bieri-Neumann-Strebel-Renz invariants, Finiteness properties, Normal subgroups, Thompson's group
1661-7207
529-570
Nucinkis, Brita E.A.
86582f48-4da6-4868-8700-d16ea4236c86
John-Green, Simon S.
76c5d69b-6e6a-4523-969d-b31c185ea237
Nucinkis, Brita E.A.
86582f48-4da6-4868-8700-d16ea4236c86
John-Green, Simon S.
76c5d69b-6e6a-4523-969d-b31c185ea237

Nucinkis, Brita E.A. and John-Green, Simon S. (2018) Quasi-automorphisms of the infinite rooted 2-edge-coloured binary tree. Groups, Geometry and Dynamics, 12 (2), 529-570. (doi:10.4171/GGD/448).

Record type: Article

Abstract

We study the groupQV , the self-maps of the infinite 2-edge coloured binary tree which preserve the edge and colour relations at cofinitely many locations. We introduce related groups QF , QT , zQ T , and zQV , prove that QF , zQ T , and zQV are of type F1, and calculate finite presentations for them. We calculate the normal subgroup structure of all 5 groups, the Bieri-Neumann-Strebel-Renz invariants of QF , and discuss the relationship of all 5 groups with other generalisations of Thompson's groups.

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More information

e-pub ahead of print date: 4 June 2018
Keywords: Bieri-Neumann-Strebel-Renz invariants, Finiteness properties, Normal subgroups, Thompson's group

Identifiers

Local EPrints ID: 424716
URI: https://eprints.soton.ac.uk/id/eprint/424716
ISSN: 1661-7207
PURE UUID: ed2dca9b-900a-41d3-bd4c-a03ef0f40f56

Catalogue record

Date deposited: 05 Oct 2018 11:41
Last modified: 05 Oct 2018 11:41

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