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
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), .
(doi:10.4171/GGD/448).
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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e-pub ahead of print date: 4 June 2018
Keywords:
Bieri-Neumann-Strebel-Renz invariants, Finiteness properties, Normal subgroups, Thompson's group
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Local EPrints ID: 424716
URI: http://eprints.soton.ac.uk/id/eprint/424716
ISSN: 1661-7207
PURE UUID: ed2dca9b-900a-41d3-bd4c-a03ef0f40f56
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Date deposited: 05 Oct 2018 11:41
Last modified: 15 Mar 2024 21:18
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Contributors
Author:
Brita E.A. Nucinkis
Author:
Simon S. John-Green
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