Networking Seifert surgeries on knots IV : Seiferters and branched coverings, Contemp
Networking Seifert surgeries on knots IV : Seiferters and branched coverings, Contemp
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网络结 Seifert 手术 IV：Seifert 和分支覆盖物，Contemp
DOI：
10.1090/conm/597/11766
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发表时间：
2013
期刊：
影响因子：
--
通讯作者：
K.Motegi
中科院分区：
文献类型：
--
作者：
A.Deruelle;M.Eudave-Munoz;K.Miyazaki;K.Motegi
Seifert 手术是对 S^3 中的结进行积分手术，产生 Seifert 纤维空间，该空间可能包含索引为 0 的特殊纤维。Seifert 手术网络是一个一维复合体，其顶点对应于 Seifert 手术；它的边缘对应于沿着“seiferters”或“环形对seiferters”的单扭曲。网络的一个问题是是否存在从每个顶点到环面结上的顶点的路径，这是最基本的 Seifert 手术。我们给出了一种寻找 Seifert 和环形 Seifert 对的方法，用于 Seifert 手术，通过采用缠结的两倍分支覆盖物获得。关于第二作者通过分支覆盖获得的三个无限系列的 Seifert 手术，我们在网络中找到了从此类手术到环面结上的 Seifert 手术的明确路径。
A Seifert surgery is an integral surgery on a knot in S^3 producing a Seifert fiber space which may contain an exceptional fiber of index 0. The Seifert Surgery Network is a 1-dimensional complex whose vertices correspond to Seifert surgeries; its edges correspond to single twistings along "seiferters" or "annular pairs of seiferters". One problem of the network is whether there is a path from each vertex to a vertex on a torus knot, the most basic Seifert surgery. We give a method to find seiferters and annular pairs of seiferters for Seifert surgeries obtained by taking two--fold branched covers of tangles. Concerning three infinite families of Seifert surgeries obtained by the second author via branched covers, we find explicit paths in the network from such surgeries to Seifert surgeries on torus knots.