CAT(0) 4-manifolds possessing a single tame point are Euclidean
CAT(0) 4-manifolds possessing a single tame point are Euclidean
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CAT(0) 拥有单个驯服点的 4-流形是欧几里得流形
DOI：
10.1007/bf02921662
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
Paul Thurston
中科院分区：
文献类型：
--
作者：
Paul Thurston
对于非正曲率空间，引入了几何柔和点和拓扑柔和点的概念。这些概念被应用于CAT(0)4-流形的刻划问题。证明了每一个具有单一(几何或拓扑)驯服点的CAT(0)M4都与R4同胚。Davis和Januszkiewicz最近构造了CAT(0)n-流形，≥5使得驯服点集形成Mn的稠密开子集，而不是Mn≠Rn。
The concepts of geometric and topological tame point are introduced for a space of nonpositive curvature. These concepts are applied to the characterization problem forCAT(0) 4-manifolds. It is shown that everyCAT(0)M4having a single (geometric or topological) tame point is homeomorphic toR4. Davis and Januszkiewicz have recently constructedCAT(0)n-manifolds,Mnwithn≥ 5 such that the set of tame points form a dense open subset ofMn, butMn≠Rn.