论文标题
灯泡技巧的新方法：4个manifolds中的磁盘
A new approach to light bulb tricks: Disks in 4-manifolds
论文作者
论文摘要
对于4个manifold $ m $和一个结$ k \ colon \ mathbb {s}^1 \ hookrightArrow \ partial m $带有双球体$ g \ colon \ colon \ colon \ colon \ mathbb {s}^2 \ hookrightArrow \ hookrightArrow \ partial m $ $ \ mathbb {d}^2 \ hookrightarrow m $带边界$ k $，使用不变回到dax。此外，我们在$ \ mathbb {d}（m; k）$上构建了一个组结构，并表明它通常既不是Abelian也不是有限生成的。我们将所有先前的结果恢复了带有框架双重球的同位素类别类别，并将$ \ mathbb {d}（m; k）$与$ m $的映射类组相关联。
For a 4-manifold $M$ and a knot $k\colon\mathbb{S}^1\hookrightarrow\partial M$ with dual sphere $G\colon\mathbb{S}^2\hookrightarrow\partial M$, we compute the set $\mathbb{D}(M;k)$ of smooth isotopy classes of neat embeddings $\mathbb{D}^2\hookrightarrow M$ with boundary $k$, using an invariant going back to Dax. Moreover, we construct a group structure on $\mathbb{D}(M;k)$ and show that it is usually neither abelian nor finitely generated. We recover all previous results for isotopy classes of spheres with framed duals and relate the group $\mathbb{D}(M;k)$ to the mapping class group of $M$.
