Characterisation of homotopy ribbon discs
Characterisation of homotopy ribbon discs
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同伦带盘的表征
DOI：
10.1016/j.aim.2021.107960
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发表时间：
2021
影响因子：
1.7
通讯作者：
Conway A
中科院分区：
文献类型：
--
作者：
Conway A
设Γ是无限循环群Z，或者是⋉-Solitar群Z[12]。设K是允许4-球中的片圆D的片纽结，其外部具有基本群Γ。我们对K的Γ-同伦带状圆盘进行了分类，直到拓扑环境同伦Rel。边界。在无限循环的情况下，存在这样的切片圆盘的唯一等价类。当Γ是BaumglagSolitar群时，至多有两个等价类的Γ-同伦带状圆盘，且对于K的Blanchfield配对的每个拉格朗日函数至多有一个这样的片圆.
Let Γ be either the infinite cyclic group Z or the Baumslag-Solitar group Z⋉ Z [1 2]. Let K be a slice knot admitting a slice disc D in the 4-ball whose exterior has fundamental group Γ. We classify the Γ-homotopy ribbon slice discs for K up to topological ambient isotopy rel. boundary. In the infinite cyclic case, there is a unique equivalence class of such slice discs. When Γ is the Baumslag-Solitar group, there are at most two equivalence classes of Γ-homotopy ribbon discs, and at most one such slice disc for each lagrangian of the Blanchfield pairing of K.