论文标题
通过拓扑同位素创建Stein表面
Creating Stein surfaces by topological isotopy
论文作者
论文摘要
我们将Freedman的拓扑结合在一起，将Eliashberg的Holomorthic理论结合在一起，以在复杂的表面构建Stein邻域系统，并使用这些理论来研究各种凸性和凹度的概念。在C^0-hall拓扑环境同位素之后，每个驯服的，拓扑嵌入的2个复合物在复杂的表面中都是一个不可超数嵌套的Stein常规街区家族的相交，这些家族都是拓扑的同位素相关性，但经常毫无疑问地意识到许多差异性类型。这些来自拓扑映射圆柱体的cantor集水平。社区的边界是只有拓扑嵌入的3个manifolds，但仍然满足了伪有的概念。这样的3个manifolds具有一定的高曲面的基本特性，这些特性在通常的平滑意义上是严格的伪有点，但它们更为普遍。拓扑假腔的互补概念是由许多差异类型的同构r^4实现的。
We combine Freedman's topology with Eliashberg's holomorphic theory to construct Stein neighborhood systems in complex surfaces, and use these to study various notions of convexity and concavity. Every tame, topologically embedded 2-complex K in a complex surface, after C^0-small topological ambient isotopy, is the intersection of an uncountable nested family of Stein regular neighborhoods that are all topologically ambiently isotopic rel K, but frequently realize uncountably many diffeomorphism types. These arise from the Cantor set levels of a topological mapping cylinder. The boundaries of the neighborhoods are 3-manifolds that are only topologically embedded, but still satisfy a notion of pseudoconvexity. Such 3-manifolds share some basic properties of hypersurfaces that are strictly pseudoconvex in the usual smooth sense, but they are far more common. The complementary notion of topological pseudoconcavity is realized by uncountably many diffeomorphism types homeomorphic to R^4.
