Almost nonnegative curvature operator and cohomology rings

被引：0
|
作者：
Herrmann, Martin [1 ,2 ]
机构：
[1] Karlsruher Inst Technol, Fak Math, Kaiserstr 89-93, D-76133 Karlsruhe, Germany
[2] Univ Munster, Math Inst, Einsteinstr 62, D-48149 Munster, Germany
来源：
FRONTIERS OF MATHEMATICS IN CHINA | 2016年 / 11卷 / 05期
关键词：
Nonnegative curvature; homogeneous spaces; curvature operator; almost nonnegative curvature; COMPACT KAHLER-MANIFOLDS; POSITIVE CURVATURE; DIFFEOMORPHISM FINITENESS; FUNDAMENTAL-GROUPS; SPLITTING THEOREM; CURVED MANIFOLDS; DIAMETER; HOMOTOPY; SPACES; BUNDLES;
D O I：
10.1007/s11464-016-0569-0
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We give a survey of results on the construction of and obstructions to metrics of almost nonnegative curvature operator on closed manifolds and results on the cohomology rings of closed, simply-connected manifolds with a lower curvature and upper diameter bound. The latter is motivated by a question of Grove whether these condition imply finiteness of rational homotopy types. This question has answers by F. Fang-X. Rong, B. Totaro and recently A. Dessai and the present author.
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页码：1259 / 1274
页数：16
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