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- Title
Torus actions, maximality, and non-negative curvature.
- Authors
Escher, Christine; Searle, Catherine
- 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.
- Subjects
TORUS; CURVATURE; SYMMETRY; SPHERES; LOGICAL prediction; ISOMETRICS (Mathematics); RIEMANNIAN manifolds
- Publication
Journal für die Reine und Angewandte Mathematik, 2021, Vol 2021, Issue 780, p221
- ISSN
0075-4102
- Publication type
Article
- DOI
10.1515/crelle-2021-0035