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Creators/Authors contains: "Amann, Manuel"

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  1. ; ; (, Mathematische Annalen)
    null (Ed.)
    Accepted Manuscript Full Text Available
  2. ; (, Communications in Contemporary Mathematics)
    Extending existing work in small dimensions, Dessai computed the Euler characteristic, signature, and elliptic genus for [Formula: see text]-manifolds of positive sectional curvature in the presence of torus symmetry. He also computes the diffeomorphism type by restricting his results to classes of manifolds known to admit non-negative curvature, such as biquotients. The first part of this paper extends Dessai’s calculations to even dimensions up to [Formula: see text]. In particular, we obtain a first characterization of the Cayley plane in such a setting. The second part studies a closely related family of manifolds called positively elliptic manifolds, and we prove a conjecture of Halperin in this context for dimensions up to [Formula: see text] or Euler characteristics up to [Formula: see text]. 
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  3. ; (, Compositio Mathematica)
    A famous conjecture of Hopf states that $$\mathbb{S}^{2}\times \mathbb{S}^{2}$$ does not admit a Riemannian metric with positive sectional curvature. In this article, we prove that no manifold product $$N\times N$$ can carry a metric of positive sectional curvature admitting a certain degree of torus symmetry. 
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  4. ; (, Algebraic & Geometric Topology)
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  5. ; (, Geometric and Functional Analysis)
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