On the Baker's map and the Simplicity of the Higher Dimensional Thompson Groups nV

TL;DR

This paper demonstrates that the baker's map can be expressed as a product of involutions, enabling a concise proof of the simplicity of higher-dimensional Thompson groups nV, extending known results efficiently.

Contribution

It shows the baker's map decomposes into involutions, allowing a short proof of the simplicity of nV groups similar to that of Thompson's V.

Findings

Baker's map is a product of involutions

Short proof of simplicity extends to higher-dimensional Thompson groups

Simplifies understanding of the structure of nV groups

Abstract

We show that the baker's map is a product of transpositions (particularly pleasant involutions), and conclude from this that an existing very short proof of the simplicity of Thompson's group V applies with equal brevity to the higher dimensional Thompson groups nV.