2024/01/02 by Jesús González, González, Jesús, José Luis León-Medina +1
Mathematics · #Geometry and complex manifolds #Advanced Combinatorial Mathematics #Mathematical Dynamics and Fractals
paper · pdf · doi:10.48550/arxiv.2401.01449
Let M(k)d(n) be the manifold of n-tuples (x1,…,xn)∈(ℝd)n having non-k-equal coordinates. We show that, for d≥2, M(3)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(\hspace.2mmℝd,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.