Higher topological complexity of Artin type groups
  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. 
Sergey Yuzvinsky
math.AT