The higher topological complexity of subcomplexes of products of spheres---and related polyhedral product spaces

Topological complexity of classical configuration spaces and related objects

“…For instance, if Γ = K n is the complete graph, then G Γ = Z n is free abelian, while if Γ has no edges, then G Γ = F n is free. For any right-angled Artin group, one has TC(G Γ ) = z(Γ ) + 1, where z(Γ ) is the maximal number of vertices of Γ covered by two (disjoint) cliques in Γ , see [9,29,31].…”