PSL(2,C), the exponential and some new free groups

TL;DR

This paper studies the structure of groups generated by PSL(2,C), the exponential map, and related transformations, revealing new algebraic properties and generalizations of previous results in group theory and topology.

Contribution

It introduces a normal form for the groupoid generated by PSL(2,C) and the exponential map, and shows the subgroup generated by positive affine maps and exponential is an HNN-extension.

Findings

Normal form for the groupoid of germs generated by PSL(2,C) and exponential

Generalization of Cohen's result on translation and power groups

The subgroup generated by positive affine maps and exponential is an HNN-extension

Abstract

We prove a normal form result for the groupoid of germs generated by PSL(2,C) and the exponential map. As consequences, we generalize a result of Cohen about the group of translations and powers, and prove that the subgroup of Homeo(R,+infinity) generated by the positive affine maps and the exponential map is isomorphic to a HNN-extension.