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Obstructions to nonnegative curvature and rational homotopy theory

Authors: Igor Belegradek and Vitali Kapovitch
Journal: J. Amer. Math. Soc. 16 (2003), 259-284
MSC (2000): Primary 53C20, 55P62
Published electronically: December 3, 2002
MathSciNet review: 1949160
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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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Additional Information

Igor Belegradek
Affiliation: Department of Mathematics, 253-37, California Institute of Technology, Pasadena, California 91125

Vitali Kapovitch
Affiliation: Department of Mathematics, University of California Santa Barbara, Santa Barbara, California 93106

Keywords: Nonnegative curvature, soul, derivation, Halperin's conjecture
Received by editor(s): October 28, 2001
Published electronically: December 3, 2002
Article copyright: © Copyright 2002 American Mathematical Society