Geometric finiteness theorems via controlled topology 4 '
Geometric finiteness theorems via controlled topology 4 '
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通过受控拓扑的几何有限性定理 4
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
Jyh
中科院分区：
文献类型：
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作者：
K. Grove;V. PeterPetersen;Jyh
这个定理的一个同伦版本在FGP [1]中得到了证明。因此，这里我们只需要考虑维度__> 4。此外，定理的最后一个主张也隐含在第一个主张中，因为当n 4= 4时，每个闭拓扑n-流形至多携带1000个光滑结构，直到n 4= 4（cf. [-KS]对于n > 5）。将定理A与Bonnet-Myers定理[ECE]和汉密尔顿关于正Ricci曲率流形的工作[H]相结合，得到Weinstein有限性定理[W]的一个推广和加强.
A homotopy version of this theorem was proved in FGP 1] for all dimensions. Here therefore, we need only consider dimensions __> 4. Moreover, the last claim of the theorem is implied by the first, since every closed topological n-manifold carries at most finitely many smooth structures up to diffeomorphism when n 4= 4 (cf. [-KS] for n > 5). Combining Theorem A with the Bonnet-Myers theorem ECE] and Hamilton's work on manifolds with positive Ricci curvature [H], yields a generalization and sharpening of Weinstein's finiteness theorem [W].