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arXiv · 1510.01908

Nonnegatively curved quotient spaces with boundary

Wolfgang Spindeler
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Abstract

Let $M$ be a compact nonnegatively curved Riemannian manifold admitting an isometric action by a compact Lie group $\mathsf G$ in a way that the quotient space $M/\mathsf G$ has nonempty boundary. Let $\pi : M \to M/\mathsf G$ denote the quotient map and $B$ be any boundary stratum of $M/\mathsf G$. Via a specific soul construction for $M/ \mathsf G$ we construct a smooth closed submanifold $N$ of $M$ such that $M \setminus \pi^{-1}(B)$ is diffeomorphic to the normal bundle of $N$. As an application we show that a simply connected torus manifold admitting an invariant metric of nonnegative curvature is rationally elliptic.

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Wolfgang Spindeler. 2015-10-07. Nonnegatively curved quotient spaces with boundary. https://arxiv.org/abs/1510.01908

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