Torus actions, maximality, and non-negative curvature
2021 ◽
Vol 0
(0)
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Keyword(s):
Abstract Let ℳ 0 n {\mathcal{M}_{0}^{n}} be the class of closed, simply connected, non-negatively curved Riemannian n-manifolds admitting an isometric, effective, isotropy-maximal torus action. We prove that if M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} , then M is equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to 3. As a special case, we then prove the Maximal Symmetry Rank Conjecture for all M ∈ ℳ 0 n {M\in\mathcal{M}_{0}^{n}} . Finally, we show the Maximal Symmetry Rank Conjecture for simply connected, non-negatively curved manifolds holds for dimensions less than or equal to 9 without additional assumptions on the torus action.
2018 ◽
Vol 61
(2)
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pp. 449-456
1988 ◽
Vol 8
(2)
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pp. 215-239
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1994 ◽
Vol 91
(1-3)
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pp. 137-142
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2010 ◽
Vol 139
(7)
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pp. 2559-2564
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