Some topologically locally-flat surfaces in the complex projective plane
Some topologically locally-flat surfaces in the complex projective plane
复制标题
复射影平面中的一些拓扑局部平坦表面
DOI：
10.1007/bf02566368
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发表时间：
1984
影响因子：
0.9
通讯作者：
L. Rudolph
中科院分区：
文献类型：
--
作者：
L. Rudolph
定理2。对于每一对大于或等于5的整数（m, n）（可能（5,5）除外），在四盘中存在一个拓扑局部平嵌曲面，其边界为类型为（m, n）的环面连杆O {m， n}，且属严格小于O {m， n}的（经典）属。在这里，如果S在M中有一个邻域N，且邻域N与S上的开放2盘束同胚，且同胚带S到一个截面上，则曲面S拓扑嵌入在4流形M中称为“拓扑局部平嵌入”。这显然是关于S嵌入M的某种局部同质性假设(例如，如果S是平滑嵌入M的，或者PL是局部平坦嵌入M的，那么它就是一个强化拓扑局部平坦嵌入。在准备本文之后，作者了解到akbulut的一个新定理——表明某些“拓扑切片”结非常类似于w中的/36，绝对不是光滑切片——这意味着并非每个拓扑局部平坦曲面都是光滑的或PL局部平坦曲面，直至全局拓扑坐标的变化。
THEOREM 2. For every pair (m, n) of integers greater than or equal to 5,(except possibly (5, 5)) there is a topologically locally-flatly embedded surface in the 4-disk with boundary a torus link O {m, n} of type (m, n) and genus strictly less than the (classical) genus of O {m, n}.Here, a surface S topologically embedded in a 4-manifold M will be called" topologically locally-flatly embedded" if S has a neighborhood N in M which is homeomorphic to an open 2-disk bundle over S by a homeomorphism carrying S to a section. This is evidently some kind of local homogeneity assumption on the embedding of S in M.(For instance, if S is smoothly, or PL locally-flatly, embedded in M then it is a fortiori topologically locally-flatly embedded. After preparing this paper, the author learned of a new theorem of Akbulut-showing that certain" topologically slice" knots very similar to/36 in w below, definitely are not smoothly slice-which implies that not every topologically locally-fiat surface is just a smooth or PL locally-fiat surface up to a global topological change of coordinates.)