Obstructions to nonnegative curvature and rational homotopy theory

By Igor Belegradek, V. Kapovitch. 2000

47 citations recorded by the source corpus.

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 x T admit no complete nonnegatively curved metrics.

Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2e162048ba576458ce86621a5b1466ccd37016ba

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. W. Ziller
2. Y. Félix

In Geometry and Topology

1. Y. Félix
2. W. Ziller
3. B. Totaro

In Mathematical Physics

1. Y. Félix
2. W. Ziller
3. B. Totaro

Citations in the corpus

• Algebraic models in geometry (2008, methodology): “Finally, we mention a result of [23] showing that not all spaces give splitting rigid triples.”
• Examples of Riemannian Manifolds with non-negative sectional curvature (2007, background): “the case where the soul is ∞at, and Belegradek-Kapovitch [BK1,’01] , [ BK2 ,’03] in general.”