论文标题
带有固定组的同质色带盘
Homotopy ribbon discs with a fixed group
论文作者
论文摘要
在拓扑类别中，当外部的基本组$ g $为$ \ mathbb {z} $和baumslag-solitar $ bs $ bs（1,2）$时，同型色带的分类是知道的。我们证明，如果一组$ g $在几何上是$ 2 $维的，并且满足了Farrell-Jones的猜想，那么涉及基本组的条件确保了与基本组$ g $的非球形同型色带的外观是S-Cobordant res。当$ g $很好时，这会导致此类光盘的分类。作为一个应用程序，对于任何打结$ j \ subset s^3 $，其结组$ g（j）$都不错，我们将补充$ g（j）$的$ j \＃-j $的同拷贝色带分类。 $ | m-n | = 1 $时，也针对$ bs（m，n）$获得了类似的应用程序。
In the topological category, the classification of homotopy ribbon discs is known when the fundamental group $G$ of the exterior is $\mathbb{Z}$ and the Baumslag-Solitar group $BS(1,2)$. We prove that if a group $G$ is geometrically $2$-dimensional and satisfies the Farrell-Jones conjecture, then a condition involving the fundamental group ensures that exteriors of aspherical homotopy ribbon discs with fundamental group $G$ are s-cobordant rel.\ boundary. When $G$ is good, this leads to the classification of such discs. As an application, for any knot $J \subset S^3$ whose knot group $G(J)$ is good, we classify the homotopy ribbon discs for $J \# -J$ whose complement has group $G(J)$. A similar application is obtained for $BS(m,n)$ when $|m-n|=1$.
