On Lusternik–Schnirelmann category and topological complexity of non-k-equal manifolds

Abstract

d (n) is rationally formal if and only if n ≤ 6. This stands in sharp contrast with the fact that all classical configuration spaces M (2) d (n) = Conf (R d , n) are rationally formal, just as are all complements of arrangements of arbitrary complex subspaces with geometric lattice of intersections. The rational non formality of M (3) d (n) for n > 6 is established via detection of non-trivial triple Massey products assessed through Poincaré duality.