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.References
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Bibliographic Information
- Igor Belegradek
- Affiliation: Department of Mathematics, 253-37, California Institute of Technology, Pasadena, California 91125
- MR Author ID: 340900
- Email: ibeleg@its.caltech.edu
- Vitali Kapovitch
- Affiliation: Department of Mathematics, University of California Santa Barbara, Santa Barbara, California 93106
- Email: vitali@math.ucsb.edu
- Received by editor(s): October 28, 2001
- Published electronically: December 3, 2002
- © Copyright 2002 American Mathematical Society
- Journal: J. Amer. Math. Soc. 16 (2003), 259-284
- MSC (2000): Primary 53C20, 55P62
- DOI: https://doi.org/10.1090/S0894-0347-02-00418-6
- MathSciNet review: 1949160