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Non-negative curvature and torus actions
Escher, Christine...

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Non-negative curvature and torus actions by Escher, Christine ( Author )
Lemonjar Open Access
Australian National University
17-08-2023
Let $\mathcal{M}_{0}^n$ be the class of closed, simply-connected, non-negatively curved Riemannian manifolds admitting an isometric, effective, isotropy-maximal torus action. We prove that if $M\in \mathcal{M}_{0}^n$, 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 three. As an immediate consequence, we prove the Maximal Symmetry Rank Conjecture for all $M\in \mathcal{M}_{0}^n$. Finally, we show the Maximal Symmetry Rank Conjecture for simply-connected, non-negatively curved manifolds holds for dimensions less than or equal to nine without assuming the torus action is almost isotropy-maximal or isotropy-maximal.
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Article
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30.00 KB
English
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MYR 0.01
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http://arxiv.org/abs/1506.08685
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