Good Groups
Good Groups
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好团体
DOI：
10.1093/oso/9780198841319.003.0019
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发表时间：
2021
期刊：
影响因子：
--
通讯作者：
Arunima Ray
中科院分区：
文献类型：
--
作者：
Min Hoon Kim;P. Orson;Junghwan Park;Arunima Ray
好的组是根据高度为1.5的带帽摸索是否包含某些类型的浸没圆盘来定义的。圆盘嵌入定理对具有良好基本群的4-流形成立。证明了无限循环群和有限群是好群，好群的扩张和上极限是好群。这表明所有初等顺从群都是好群。证明中使用了高度的提升和收缩，并分析了基本群元素在这些操作下的行为。拓扑4-流形研究中的一个中心开放问题是精确确定哪些群是好的。
Good groups are defined in terms of whether capped gropes of height 1.5 contain certain types of immersed discs. The disc embedding theorem holds for 4-manifolds with good fundamental group. It is proven that the infinite cyclic group and finite groups are good, and that extensions and colimits of good groups are good. This shows that all elementary amenable groups are good. The proofs use grope height raising and contraction, together with an analysis of how fundamental group elements behave under these operations. A central open problem in the study of topological 4-manifolds is to determine precisely which groups are good.