Gespeichert in:
| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2401.01449 |
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Inhaltsangabe:
- Let $M^{(k)}_{d}(n)$ be the manifold of $n$-tuples $(x_1,\ldots,x_n)\in(\mathbb{R}^d)^n$ having non-$k$-equal coordinates. We show that, for $d\geq2$, $M^{(3)}_{d}(n)$ is rationally formal if and only if $n\leq 6$. This stands in sharp contrast with the fact that all classical configuration spaces $M^{(2)}_d(n)=\text{Conf}(\hspace{.2mm}\mathbb{R}^d,n)$ 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.