Classifying spaces for the family of virtually cyclic subgroups of braid groups

TL;DR

This paper determines the minimal dimension of classifying spaces for braid groups with respect to virtually cyclic subgroups, establishing it as equal to the number of strands for all n ≥ 3.

Contribution

It proves that the minimal dimension of such classifying spaces for both full and pure braid groups is exactly n, for all n ≥ 3.

Findings

Minimal dimension of classifying space for B_n and P_n is n

Dimension result holds for all n ≥ 3

Provides a precise geometric invariant for braid groups

Abstract

We prove that, for $n\geq 3$, the minimal dimension of a model of the classifying space of the full braid group $B_n$, and of the pure braid group $P_n$, with respect to the family of virtually cyclic groups is $n$.