Obstructions to nonnegative curvature and rational homotopy theory

Belegradek, Igor; Kapovitch, Vitali

doi:10.1090/S0894-0347-02-00418-6

Obstructions to nonnegative curvature and rational homotopy theory
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by Igor Belegradek and Vitali Kapovitch

J. Amer. Math. Soc. 16 (2003), 259-284

DOI: https://doi.org/10.1090/S0894-0347-02-00418-6

Published electronically: December 3, 2002

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Abstract:

We establish a link between rational homotopy theory and the problem which vector bundles admit a complete Riemannian metric of nonnegative sectional curvature. As an application, we show for a large class of simply-connected nonnegatively curved manifolds that, if $C$ lies in the class and $T$ is a torus of positive dimension, then “most” vector bundles over $C\times T$ admit no complete nonnegatively curved metrics.

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