Obstructions to nonnegative curvature and rational homotopy theory |
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Authors: | Igor Belegradek Vitali Kapovitch |
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Institution: | Department of Mathematics, 253-37, California Institute of Technology, Pasadena, California 91125 ; Department of Mathematics, University of California Santa Barbara, Santa Barbara, California 93106 |
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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 lies in the class and is a torus of positive dimension, then ``most' vector bundles over admit no complete nonnegatively curved metrics. |
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Keywords: | Nonnegative curvature soul derivation Halperin's conjecture |
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