Higher topological complexity of Artin type groups

TL;DR

This paper computes the higher topological complexity of pure Artin type groups associated with complex reflection arrangements, providing a combinatorial criterion that simplifies cohomological calculations.

Contribution

It introduces a combinatorial criterion that ensures the cohomological lower bound matches the dimensional upper bound for TC_s of these groups.

Findings

Calculated TC_s for pure Artin groups of all finite complex reflection groups.

Established a combinatorial criterion for arrangements to simplify topological complexity computations.

Provided explicit formulas or bounds for the topological complexity of these groups.

Abstract

We calculate the higher topological complexity TC$_s$ for the complements of reflection arrangements, in other words for the pure Artin type groups of all finite complex reflection groups. In order to do that we introduce a simple combinatorial criterion of arrangements sufficed for the cohomological low bound for TC$_s$ to coincide with the dimensional upper bound.