Line and Hyperplane GT-variants

TL;DR

This paper introduces a new variant of the Grothendieck-Teichmüller group based on hyperplane arrangements and fundamental groups, proving its isomorphism to the absolute Galois group of b.

Contribution

It defines a novel variant of the Grothendieck-Teichmüller group and establishes its isomorphism with the absolute Galois group of b.

Findings

New variant of Grothendieck-Teichmüller group introduced

Proves isomorphism to the absolute Galois group of b

Links hyperplane arrangements with fundamental groups and Galois theory

Abstract

In this work, we introduce a variant of the Grothendieck-Teichm{\"u}ller group, defined in terms of complements of hyperplane arrangements and pro-$\ell$ two-step nilpotent fundamental groups, and prove that it is isomorphic to the absolute Galois group of $\Qbb$.