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Topological obstructions to nonnegative curvature

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Abstract.

We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit no nonnegatively curved metrics.

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Authors and Affiliations

  1. Department of Mathematics 253-37, California Institute of Technology, Pasadena, CA 91125, USA (e-mail: ibeleg@its.caltech.edu) , , , , , , US

    Igor Belegradek

  2. Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104, USA (e-mail: vitali@math.upenn.edu) , , , , , , US

    Vitali Kapovitch

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  1. Igor Belegradek
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  2. Vitali Kapovitch
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Received February 11, 2000 / Published online February 5, 2001

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Belegradek, I., Kapovitch, V. Topological obstructions to nonnegative curvature. Math Ann 320, 167–190 (2001). https://doi.org/10.1007/PL00004467

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  • DOI: https://doi.org/10.1007/PL00004467

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