Higher topological complexity of Artin type 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.

8 pages, a talk given by the author at the conference "Configuration Spaces" in Cortona in September of 2014