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Cohomogeneity-two torus actions on non-negatively curved manifolds of low dimension

Galaz-Garcia, Fernando and Kerin, Martin (2014) 'Cohomogeneity-two torus actions on non-negatively curved manifolds of low dimension.', Mathematische Zeitschrift, 276 (1-2). pp. 133-152.

Abstract

Let Mn, n ∈ {4, 5, 6}, be a compact, simply connected n-manifold which admits some Riemannian metric with non-negative curvature and an isometry group of maximal possible rank. Then any smooth, effective action on Mn by a torus Tn−2 is equivariantly diffeomorphic to an isometric action on a normal biquotient. Furthermore, it follows that any effective, isometric circle action on a compact, simply connected, nonnegatively curved four-dimensional manifold is equivariantly diffeomorphic to an effective, isometric action on a normal biquotient.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1007/s00209-013-1190-5
Publisher statement:This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00209-013-1190-5
Date accepted:12 May 2013
Date deposited:15 November 2022
Date of first online publication:11 July 2013
Date first made open access:15 November 2022

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