On the cohomology rings of holomorphically fillable manifolds
On the cohomology rings of holomorphically fillable manifolds
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关于全纯可充流形的上同调环
DOI：
10.1090/conm/475/09282
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Patrick Popescu
中科院分区：
文献类型：
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作者：
Patrick Popescu
如果奇维可微流形与紧致强伪凸复流形的边界微分同胚，则称为\{全纯可填充}，如果最后一个流形可以选择为Stein，则称为\{Stein可填充}，如果它是微分同胚的，则称为\{Milnor可填充}正常复解析空间的孤立奇异性的抽象边界。我们证明了维数至少为4的边界流形的同伦维数限制了其边界的上同调环（具有任何系数）。这给出了限制上同调环的斯坦可填充流形，对尺寸的例外轨迹的任何决议的一个给定的孤立奇点，和拓扑的光滑奇点。我们还给出了Durfee &海恩和Bungart关于Milnor可充流形和全纯可充流形的上同调环的结构定理的新证明。本文给出的各种结构定理意味着在至少5维空间中，Stein可填充流形、Milnor可填充流形和全纯可填充流形是两两不同的。
An odd-dimensional differentiable manifold is called \emph{holomorphically fillable} if it is diffeomorphic to the boundary of a compact strongly pseudoconvex complex manifold, \emph{Stein fillable} if this last manifold may be chosen to be Stein and \emph{Milnor fillable} if it is diffeomorphic to the abstract boundary of an isolated singularity of normal complex analytic space. We show that the homotopical dimension of a manifold-with-boundary of dimension at least 4 restricts the cohomology ring (with any coefficients) of its boundary. This gives restrictions on the cohomology rings of Stein fillable manifolds, on the dimension of the exceptional locus of any resolution of a given isolated singularity, and on the topology of smoothable singularities. We give also new proofs of structure theorems of Durfee & Hain and Bungart about the cohomology rings of Milnor fillable and respectively holomorphically fillable manifolds. The various structure theorems presented in this paper imply that in dimension at least 5, the classes of Stein fillable, Milnor fillable and holomorphically fillable manifolds are pairwise different.
DOI：
10.1090/pspum/052.2
发表时间：
1991
期刊：
--
影响因子：
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作者：
Eric Bedford;J. D'Angelo;R. Greene;S. Krantz
通讯作者：
Eric Bedford;J. D'Angelo;R. Greene;S. Krantz