Skip to Main Content

Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Obstructions to nonnegative curvature and rational homotopy theory
HTML articles powered by AMS MathViewer

by Igor Belegradek and Vitali Kapovitch PDF
J. Amer. Math. Soc. 16 (2003), 259-284 Request permission

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
Similar Articles
  • Retrieve articles in Journal of the American Mathematical Society with MSC (2000): 53C20, 55P62
  • Retrieve articles in all journals with MSC (2000): 53C20, 55P62
Additional 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