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• W2091737269 abstract "In this paper, we first prove that any closed simply connected 4-manifold that admits a decomposition into two disk bundles of rank greater than 1 is diffeomorphic to one of the standard elliptic 4-manifolds: $$mathbb {S}^4$$ , $$mathbb {CP}^2$$ , $$mathbb {S}^2times mathbb {S}^2$$ , or $$mathbb {CP}^2$$ # $$pm mathbb {CP}^2$$ . As an application we prove that any closed simply connected 4-manifold admitting a nontrivial singular Riemannian foliation is diffeomorphic to a connected sum of copies of standard $$mathbb {S}^4$$ , $$pm mathbb {CP}^2$$ and $$mathbb {S}^2times mathbb {S}^2$$ . A classification of singular Riemannian foliations of codimension 1 on all closed simply connected 4-manifolds is obtained as a byproduct. In particular, there are exactly 3 non-homogeneous singular Riemannian foliations of codimension 1, complementing the list of cohomogeneity one 4-manifolds." @default.
• W2091737269 created "2016-06-24" @default.
• W2091737269 creator A5004236714 @default.
• W2091737269 creator A5080557962 @default.
• W2091737269 date "2015-02-11" @default.
• W2091737269 modified "2023-10-17" @default.
• W2091737269 title "Differentiable classification of 4-manifolds with singular Riemannian foliations" @default.
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• W2091737269 doi "https://doi.org/10.1007/s00208-015-1172-5" @default.
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