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arXiv · 1302.4593

Singular Riemannian foliations and applications to positive and nonnegative curvature

Fernando Galaz-Garcia·Marco Radeschi
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Abstract

We determine the structure of the fundamental group of the regular leaves of a closed singular Riemannian foliation on a compact, simply connected Riemannian manifold. We also study closed singular Riemannian foliations whose leaves are homeomorphic to aspherical or to Bieberbach manifolds. These foliations, which we call A-foliations and B-foliations, respectively, generalize isometric torus actions on Riemannian manifolds. We apply our results to the classification problem of compact, simply connected Riemannian 4- and 5-manifolds with positive or nonnegative sectional curvature.

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Fernando Galaz-Garcia, Marco Radeschi. 2015-02-22. Singular Riemannian foliations and applications to positive and nonnegative curvature. https://doi.org/10.1112/jtopol%2Fjtv004

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