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Creators/Authors contains: "Escher, Christine"

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  1. ; ; (, Transactions of the American Mathematical Society)
    We extend the equivariant classification results of Escher and Searle for closed, simply connected, Riemannian n n -manifolds with non-negative sectional curvature admitting isometric isotropy-maximal torus actions to the class of such manifolds admitting isometric strictly almost isotropy-maximal torus actions. In particular, we prove that any such manifold is equivariantly diffeomorphic to the free, linear quotient by a torus of a product of spheres of dimensions greater than or equal to three. 
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  2. ; ; (, International Mathematics Research Notices)
    Abstract Let $$M$$ be a closed, odd GKM$$_3$$ manifold of non-negative sectional curvature. We show that in this situation one can associate an ordinary abstract GKM$$_3$$ graph to $$M$$ and prove that if this graph is orientable, then both the equivariant and the ordinary rational cohomology of $$M$$ split off the cohomology of an odd-dimensional sphere. 
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  3. ; (, Journal für die reine und angewandte Mathematik (Crelles Journal))
    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 showthe 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. 
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