The affine Artin group of type $\widetilde B_n$ is virtually poly-free

TL;DR

This paper proves that the affine Artin group of type B_n is virtually poly-free and offers an alternative solution to the K(,) problem for this group, advancing understanding in geometric group theory.

Contribution

It establishes the virtual poly-freeness of the affine Artin group B_n and provides a new approach to the K(,) problem for these groups.

Findings

Affine Artin group B_n is virtually poly-free

Provides an alternative solution to the K(,) problem for B_n

Advances understanding of the topology and algebraic structure of affine Artin groups

Abstract

In this note we prove that the affine Artin group of type $\widetilde B_n$ is virtually poly-free. The proof also gives another solution of the $K(\pi, 1)$ problem for $\widetilde B_n$.