Differentiable classification of 4-manifolds with singular Riemannian foliations

作者：Ge Jianquan^*; Radeschi Marco

来源：Mathematische Annalen, 2015, 363(1-2): 525-548.

DOI：10.1007/s00208-015-1172-5

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: , , , or #. 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 , and . 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.

• 出版日期2015-10
• 单位北京师范大学