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$\mathbb{R}$--trees and accessibility over arc-stabilisers

Elia Fioravanti

Abstract

Let $G\curvearrowright T$ be a minimal action on an $\mathbb{R}$--tree with $G$ finitely presented. Assuming that $G$ is accessible over the family of arc-stabilisers of $T$, we give a description of the point-stabilisers of $T$ in terms of simplicial trees. In particular, these point-stabilisers are finitely generated. This has applications to the study of automorphisms of right-angled Artin groups and special groups.

$\mathbb{R}$--trees and accessibility over arc-stabilisers

Abstract

Let be a minimal action on an --tree with finitely presented. Assuming that is accessible over the family of arc-stabilisers of , we give a description of the point-stabilisers of in terms of simplicial trees. In particular, these point-stabilisers are finitely generated. This has applications to the study of automorphisms of right-angled Artin groups and special groups.
Paper Structure (9 sections, 15 theorems, 1 equation)

This paper contains 9 sections, 15 theorems, 1 equation.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Generalities
  4. Accessibility
  5. Refinements, collapses, deformation spaces
  6. The main theorem
  7. Special groups
  8. Convex-cocompactness
  9. Special groups and real trees

Key Result

Theorem 1

Let $G$ be finitely presented and torsion-free. Let $G\curvearrowright T$ be a minimal $\mathbb{R}$--tree, and let $\mathcal{F}$ be the family of $G$--stabilisers of arcs of $T$. Suppose that all the following are satisfied. Then all of the following hold.

Theorems & Definitions (31)

  • Theorem 1
  • Corollary 2
  • Lemma 2.1
  • Lemma 2.2
  • proof
  • Lemma 2.3
  • Lemma 2.4
  • proof
  • Lemma 2.5
  • proof
  • ...and 21 more