Nilpotency, almost nonnegative curvature, and the gradient flow on Alexandrov spaces

• 成果类型: Article
• 署名作者: Kapovitch, Vitali; Petrunin, Anton; Tuschmann, Wilderich
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2010.171.343
• 发表日期: 2010
• 页码: 343-373
• 关键词: fundamental-groups; MANIFOLDS

摘要

We show that almost nonnegatively curved m-manifolds are, up to finite cover, nilpotent spaces in the sense of homotopy theory and have C(m)-nilpotent fundamental groups. We also show that up to a finite cover almost nonnegatively curved manifolds are fiber bundles with simply connected fibers over nilmanifolds.