New topologically slice knots
New topologically slice knots
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新的拓扑切片结
DOI：
10.2140/gt.2005.9.2129
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发表时间：
2005
影响因子：
2
通讯作者：
P. Teichner
中科院分区：
文献类型：
--
作者：
Stefan Friedl;P. Teichner
1980 年代初期，Mike Freedman 证明所有具有平凡亚历山大多项式的结都是拓扑切片（具有基本群 Z）。本文包含第一个拓扑切片结的新例子。事实上，我们给出了一个充分的同调条件，在该条件下，结是基本群 Z ⋉ Z[1/2] 的切片。已知这两个基本群是唯一可解的带状群。我们的同调条件意味着亚历山大多项式等于 (t − 2)(t 1 − 2)，但也包含有关结补的元布尔覆盖的信息（因为该亚历山大多项式存在许多非切片结）。
In the early 1980’s Mike Freedman showed that all knots with trivial Alexander polynomial are topologically slice (with fundamental group Z). This paper contains the first new examples of topologically slice knots. In fact, we give a sufficienthomological condition under which a knot is slice with fundamental group Z ⋉ Z[1/2]. These two fundamental groups are known to be the only solvable ribbon groups. Our homological condition implies that the Alexander polynomial equals (t − 2)(t 1 − 2) but also contains information about the metabelian cover of the knot complement (since there are many non-slice knots with this Alexander polynomial).