Non-nesting actions of groups on real trees vs isometric actions

TL;DR

This paper investigates non-nesting group actions on R-trees and demonstrates that under certain natural conditions, these actions are equivalent to isometric actions, with applications to various classes of groups.

Contribution

It establishes conditions under which non-nesting actions on R-trees are actually isometric, extending understanding of group actions in geometric group theory.

Findings

Non-nesting actions can be equivalent to isometric actions under certain conditions.

Applications to permutation groups, linear groups, and Polish groups.

Provides criteria linking group generation properties to action types.

Abstract

We study non-nesting actions on R-trees. We prove that some natural conditions describing how the group is generated, imply that such an action involves an isometric action on an R-tree. This can be applied to permutation groups, linear groups and some Polish groups.