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

被引：32
|
作者：
Kapovitch, Vitali [1 ]
Petrunin, Anton [2 ]
Tuschmann, Wilderich [3 ]
机构：
[1] Univ Toronto, Dept Math, Toronto, ON M5S 2E4, Canada
[2] Penn State Univ, Dept Math, University Pk, PA 16802 USA
[3] Univ Kiel, D-24118 Kiel, Germany
来源：
ANNALS OF MATHEMATICS | 2010年 / 171卷 / 01期
基金：
美国国家科学基金会;
关键词：
FUNDAMENTAL-GROUPS; MANIFOLDS;
D O I：
10.4007/annals.2010.171.343
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
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.
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页码：343 / 373
页数：31
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