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

Galaz-Garcia, Fernando; Kerin, Martin

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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.

Citation

Galaz-Garcia, F., & Kerin, M. (2014). Cohomogeneity-two torus actions on non-negatively curved manifolds of low dimension. Mathematische Zeitschrift, 276(1-2), 133-152. https://doi.org/10.1007/s00209-013-1190-5

Journal Article Type Article
Acceptance Date May 12, 2013
Online Publication Date Jul 11, 2013
Publication Date 2014-02
Deposit Date Dec 12, 2019
Publicly Available Date Nov 15, 2022
Journal Mathematische Zeitschrift
Print ISSN 0025-5874
Electronic ISSN 1432-1823
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 276
Issue 1-2
Pages 133-152
DOI https://doi.org/10.1007/s00209-013-1190-5
Related Public URLs https://arxiv.org/abs/1111.1640

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Copyright 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




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