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.
Rakuten Institute of Technology, Rakuten, Inc
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Survey of gauge theory for families with focus on applications to diffeomorphism groups of 4-manifolds developed 2021-2025.
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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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Diffeomorphism groups and gauge theory for families
Survey of gauge theory for families with focus on applications to diffeomorphism groups of 4-manifolds developed 2021-2025.
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Gauge theory for families
A survey of gauge theory for families and its applications to comparing diffeomorphism and homeomorphism groups of 4-manifolds up to 2021.