JournalsggdVol. 12, No. 2pp. 529–570

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

  • Brita E. A. Nucinkis

    Royal Holloway, University of London, Egham, UK
  • Simon St. John-Green

    University of Southampton, UK
Quasi-automorphisms of the infinite rooted 2-edge-coloured binary tree cover
Download PDF

A subscription is required to access this article.

Abstract

We study the group QVQV, the self-maps of the infinite 22-edge coloured binary tree which preserve the edge and colour relations at cofinitely{\vadj2} many locations. We introduce related groups QFQF, QTQT, \wtildeQT\wtilde{Q}T, and \wtildeQV\wtilde{Q}V, prove that QFQF, \wtildeQT\wtilde{Q}T, and \wtildeQV\wtilde{Q}V are of type \F\F_\infty, and calculate finite presentations for them. We calculate the normal subgroup structure of all 55 groups, the Bieri–Neumann–Strebel–Renz invariants of QFQF, and discuss the relationship of all 55 groups with other generalisations of Thompson's groups.

Cite this article

Brita E. A. Nucinkis, Simon St. John-Green, Quasi-automorphisms of the infinite rooted 2-edge-coloured binary tree. Groups Geom. Dyn. 12 (2018), no. 2, pp. 529–570

DOI 10.4171/GGD/448