Hairy graph construction yields nontrivial rational homotopy classes proving infinite-dimensionality of π_•(Emb_c(R^{n-2}, R^n)) ⊗ Q for odd n ≥ 5.
The cohomology ring of the co lored braid group
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Non-3-equal manifolds M^(3)_d(n) are rationally formal if and only if n ≤ 6 for d ≥ 2.
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Infinite-dimensionality of the rational homotopy groups of the space of long embeddings of codimension 2
Hairy graph construction yields nontrivial rational homotopy classes proving infinite-dimensionality of π_•(Emb_c(R^{n-2}, R^n)) ⊗ Q for odd n ≥ 5.
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The rational (non-)formality of the non-3-equal manifolds
Non-3-equal manifolds M^(3)_d(n) are rationally formal if and only if n ≤ 6 for d ≥ 2.