{"paper":{"title":"Nonnegatively curved quotient spaces with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Wolfgang Spindeler","submitted_at":"2015-10-07T12:03:02Z","abstract_excerpt":"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 cur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.01908","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}