Nonconcordant links with homology cobordant zero-framed surgery manifolds
Nonconcordant links with homology cobordant zero-framed surgery manifolds
复制标题
与同源协调零框架手术流形的非协调链接
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
Mark Powell
中科院分区：
文献类型：
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作者：
Jae Choon Cha;Mark Powell
通过保持子午线同伦类的拓扑同调余边，利用四维拓扑运算，给出了3-连环的零标架运算流形同调于3-环面的充分条件，而3-环环是由Borroean环上的零标架运算产生的。这使得我们能够给出具有未打结的分支和消失的成对连接数的3-分支环的新例子，使得这些环中的任何两个在上述意义下具有同调余界零运算，但零运算流形不是同胚的。此外，这些链节彼此并不协调，事实上，对于至少为3的每个n，它们可以被选择为高度n而不是高度n+1对称摸索协调。
We use topological surgery in dimension four to give sufficient conditions for the zero framed surgery manifold of a 3-component link to be homology cobordant to the 3-torus, which arises from zero framed surgery on the Borromean rings, via a topological homology cobordism preserving the homotopy classes of the meridians. This enables us to give new examples of 3-component links with unknotted components and vanishing pairwise linking numbers, such that any two of these links have homology cobordant zero surgeries in the above sense, but the zero surgery manifolds are not homeomorphic. Moreover the links are not concordant to one another, and in fact they can be chosen to be height n but not height n+1 symmetric grope concordant, for each n which is at least three.