Nonnegatively curved quotient spaces with boundary

  • Wolfgang Spindeler
Original Article


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 \(\pi : M \rightarrow M/\mathsf {G}\) 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.

Mathematics Subject Classification




I am grateful to Burkhard Wilking for his support during the work on my thesis where the techniques developed here originate.


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Copyright information

© Sociedad Matemática Mexicana 2019

Authors and Affiliations

  1. 1.DüsseldorfGermany

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