Every Contact Manifolds can be given a Nonfillable Contact Structure
Every Contact Manifolds can be given a Nonfillable Contact Structure
复制标题
DOI：
10.1093/imrn/rnm115
复制
发表时间：
2006-08
影响因子：
1
通讯作者：
K. Niederkruger;O. Koert
中科院分区：
文献类型：
--
作者：
K. Niederkruger;O. Koert
最近，Francisco Presas Mata 构建了第一个尺寸大于 3 的闭合接触流形示例，其中包含塑料材料，因此是不可填充的。在他的例子中使用接触手术，我们在每个球体 S^{2n-1}, n>1 上创建了一个奇异的接触结构 \xi_-，它也包含塑料。因此，每个闭接触流形 M（S^1 除外）都可以通过取 M 与 (S^{2n-1},\xi_-) 的连通和来转换为不可（半正）可填充的接触流形。
Recently Francisco Presas Mata constructed the first examples of closed contact manifolds of dimension larger than 3 that contain a plastikstufe, and hence are non-fillable. Using contact surgery on his examples we create on every sphere S^{2n-1}, n>1, an exotic contact structure \xi_- that also contains a plastikstufe. As a consequence, every closed contact manifold M (except S^1) can be converted into a contact manifold that is not (semi-positively) fillable by taking the connected sum of M with (S^{2n-1},\xi_-).