Obstructions to nonnegative curvature and rational homotopy theory-Reference-Cited by-同舟云学术

Obstructions to nonnegative curvature and rational homotopy theory

Published:2002-12-03 Issue:2 Volume:16 Page:259-284
ISSN:0894-0347
Container-title:Journal of the American Mathematical Society
language:en
Short-container-title:J. Amer. Math. Soc.

Author:

Belegradek Igor,Kapovitch Vitali

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 C lies in the class and T T is a torus of positive dimension, then “most” vector bundles over C × T C\times T admit no complete nonnegatively curved metrics.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/jams/2003-16-02/S0894-0347-02-00418-6/S0894-0347-02-00418-6.pdf

Reference36 articles.

1. On a family of 13-dimensional closed Riemannian manifolds of positive curvature;Bazaĭkin, Ya. V.;Sibirsk. Mat. Zh.,1996

2. [BK]BK2 I. Belegradek and V. Kapovitch, Obstructions to nonnegative curvature and rational homotopy theory, preprint, 2000, available electronically at the xxx-achive: http://arxiv.org/abs/math.DG/0007007.

3. Finiteness theorems for nonnegatively curved vector bundles;Belegradek, Igor;Duke Math. J.,2001

4. Topological obstructions to nonnegative curvature;Belegradek, Igor;Math. Ann.,2001

5. On the structure of complete manifolds of nonnegative curvature;Cheeger, Jeff;Ann. of Math. (2),1972

Cited by 13 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Higher Nash blow-up local algebras of singularities and its derivation Lie algebras;Journal of Algebra;2023-03

2. Vector bundles of non-negative curvature over cohomogeneity one manifolds;Advances in Mathematics;2022-08

3. Positive weights and self-maps;Proceedings of the American Mathematical Society;2022-04-29

4. Non-existence of negative weight derivations on positively graded Artinian algebras;Transactions of the American Mathematical Society;2019-03-20

5. A note on the Petersen-Wilhelm conjecture;Proceedings of the American Mathematical Society;2018-07-05