Explicit chain complexes and spectral sequences compute homology of configuration spaces in positive characteristic, lifting Knudsen's theorem, with a conjecture on twisted coalgebra equivalences implying homotopy invariance.
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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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Homology of configuration spaces in positive characteristic via point-set constructions
Explicit chain complexes and spectral sequences compute homology of configuration spaces in positive characteristic, lifting Knudsen's theorem, with a conjecture on twisted coalgebra equivalences implying homotopy invariance.
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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.