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Obstructions to nonnegative curvature and rational homotopy theory

Igor Belegradek·Vitali Kapovitch
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Abstract

We establish a link between rational homotopy theory and the problem which vector bundles admit 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 the product of C and T admit no complete nonnegatively curved metric.

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Igor Belegradek, Vitali Kapovitch. 2000-07-01. Obstructions to nonnegative curvature and rational homotopy theory. https://arxiv.org/abs/math/0007007

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