Fundamental groups of manifolds with positive sectional curvature and torus symmetry
arXiv:1310.7251
Abstract
In 1965, S.-S. Chern posed a question concerning the extent to which fundamental groups of manifolds admitting positive sectional curvature look like spherical space form groups. The original question was answered in the negative by Shankar in 1998, but there are a number of positive results in the presence of symmetry. These classifications fall into categories according to the strength of their conclusions. We give an overview of these results in the case of torus symmetry and prove new results in each of these categories.
This article updates and replaces version 1, which is titled "On the Chern problem with symmetry". Introduction and organization have been improved and proofs have been streamlined using the results of the preprint arXiv:1402.7255. The results are improved in some cases but otherwise left unchanged
References in corpus (6)
- Examples of Riemannian Manifolds with non-negative sectional curvature
- An exotic sphere with positive sectional curvature
- Nonnegatively and Positively curved manifolds
- An exotic sphere with positive curvature
- Positively curved metrics on symmetric spaces with large symmetry rank
- Positive curvature and the elliptic genus