2-complexes with unique embeddings in 3-space
2-complexes with unique embeddings in 3-space
复制标题
3 空间中具有独特嵌入的 2 复合体
DOI：
10.1112/blms.12718
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发表时间：
2022
影响因子：
0.9
通讯作者：
Georgakopoulos A
中科院分区：
文献类型：
--
作者：
Georgakopoulos A
一个著名的惠特尼定理指出，一个3连通的平面图形承认一个本质上唯一的嵌入到2球中。我们证明了一个三维类比：一个单连通的2 -复3连通的每连杆图承认一个本质上唯一的局部平面嵌入到3球中，如果它承认的话。这可以看作是三维舍恩菲斯定理的推广。
A well‐known theorem of Whitney states that a 3‐connected planar graph admits an essentially unique embedding into the 2‐sphere. We prove a 3‐dimensional analogue: a simply‐connected 2‐complex every link graph of which is 3‐connected admits an essentially unique locally flat embedding into the 3‐sphere, if it admits one at all. This can be thought of as a generalisation of the 3‐dimensional Schoenflies theorem.