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Award ID contains: 1404670

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  1. ; (, Algebraic & Geometric Topology)
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  2. (, Commentarii Mathematici Helvetici)
    We prove an obstruction at the level of rational cohomology to the existence of positively curved metrics with large symmetry rank. The symmetry rank bound is logarithmic in the dimension of the manifold. As one application, we provide evidence for a generalized conjecture of H. Hopf, which states that no symmetric space of rank at least two admits a metric with positive curvature. Other applications concern product manifolds, connected sums, and manifolds with nontrivial fundamental group. 
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  3. ; (, Geometric and Functional Analysis)
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