Obstructions to nonnegative curvature and rational homotopy theory
Differential Geometry
2017-09-11 v4 Algebraic Topology
Abstract
We establish a link between rational homotopy theory and the problem which vector bundles admit 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 the product of C and T admit no complete nonnegatively curved metric.
Keywords
Cite
@article{arxiv.math/0007007,
title = {Obstructions to nonnegative curvature and rational homotopy theory},
author = {Igor Belegradek and Vitali Kapovitch},
journal= {arXiv preprint arXiv:math/0007007},
year = {2017}
}
Comments
Fixed an error is the proof of lemma B.1