Conjugation-invariant norms on the commutator subgroup of the infinite braid group

TL;DR

This paper proves that the commutator subgroup of the infinite braid group admits stably unbounded norms and shows these norms are equivalent to previously studied biinvariant word norms.

Contribution

It provides a new proof of the unboundedness of norms on the commutator subgroup and establishes their equivalence to known biinvariant word norms.

Findings

The commutator subgroup admits stably unbounded norms.

Constructed norms are equivalent to biinvariant word norms.

Supports the understanding of algebraic structures in infinite braid groups.

Abstract

In this paper, we give a proof of the result of Brandenbursky and K\c{e}dra which says that the commutator subgroup of the infinite braid group admits stably unbounded norms. Moreover, we observe the norms which we constructed are equivalent to the biinvariant word norm studied by Brandenbursky and K\c{e}dra.