具有指定亏格的稠密端集的Simply Connected 3-流形
Simply Connected 3-Manifolds with a Dense Set of Ends of Specified Genus
摘要：
我们证明了对于每个序列$(n_i)$，其中每个$n_i$是大于1的整数或者是$\infty$，存在一个单连通开3-流形$M$，其具有可数稠密的端集$\{e_i\}$，使得对于每个$i$，端$e_i$的亏格等于$n_i$。此外，亏格的结束，而不是在密集集被证明是小于或等于2。这些单连通3-流形被构造为$S^3$中某些Cantor集的补。所使用的方法需要仔细分析的结束和新的技术处理无限亏格的属。
英文摘要：
We show that for every sequence $(n_i)$, where each $n_i$ is either an integer greater than 1 or is $\infty$, there exists a simply connected open 3-manifold $M$ with a countable dense set of ends $\{e_i\}$ so that, for every $i$, the genus of end $e_i$ is equal to $n_i$. In addition, the genus of the ends not in the dense set is shown to be less than or equal to 2. These simply connected 3-manifolds are constructed as the complements of certain Cantor sets in $S^3$. The methods used require careful analysis of the genera of ends and new techniques for dealing with infinite genus.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
