The subgroup $PSL(2,R)$ is spherical in the group of diffeomorphisms of the circle

TL;DR

This paper proves that the subgroup PSL(2,R) is spherical within the group of C^3-diffeomorphisms of the circle, and similarly, automorphisms of a Bruhat--Tits tree are spherical in hierarchomorphisms.

Contribution

It establishes the sphericity of PSL(2,R) in diffeomorphisms of the circle and automorphisms of Bruhat--Tits trees within hierarchomorphisms.

Findings

PSL(2,R) is a spherical subgroup in the group of C^3-diffeomorphisms of the circle

Automorphisms of a Bruhat--Tits tree form a spherical subgroup in hierarchomorphisms

Provides new insights into subgroup structures in diffeomorphism and hierarchomorphism groups

Abstract

We show that the group $PSL(2,R)$ is a spherical subgroup in the group of $C^3$-diffeomorphisms of the circle. Also, the group of automorphisms of a Bruhat--Tits tree is a spherical subgroup in the group of hierarchomorphisms of the tree.