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- W2953200630 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: $mathbb{S}^4$, $mathbb{CP}^2$, $mathbb{S}^2timesmathbb{S}^2$, 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 $mathbb{S}^4$, $pmmathbb{CP}^2$ and $mathbb{S}^2timesmathbb{S}^2$. 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.
- W2953200630 created "2019-06-27" @default.
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- W2953200630 date "2013-12-02" @default.
- W2953200630 modified "2023-09-26" @default.
- W2953200630 title "Differentiable classification of 4-manifolds with singular Riemannian foliations" @default.
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- W2953200630 doi "https://doi.org/10.48550/arxiv.1312.0667" @default.
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