论文标题
紧凑拓扑歧管同态组的有限亚组几乎是nilpotent
Finite subgroups of the homeomorphism group of a compact topological manifold are almost nilpotent
论文作者
论文摘要
大约二十年前，吉斯（Ghys）猜想，紧凑型歧管M的二型型组的有限亚组具有一个ABELIAN正常的索引索引，A（m）仅取决于M。在我们在Arxiv Ghys上的反例首次出现之后，提出了修订的猜想，该猜想仅预测最多n（m）的nilpotent nilpotent forman子组。我们的主要结果是修订后的Ghys猜想的证明。更普遍地，我们表明，同样的结果与具有有限生成的同源性组的同态组合群相同。我们的证明是基于有限的群体理论结果，该结果为证明类似的Jordan型定理提供了一般策略。
Around twenty years ago Ghys conjectured that finite subgroups of the diffeomorphism group of a compact smooth manifold M have an abelian normal subgroup of index at most a(M), where a(M) depends only on M. First we construct a family of counterexamples to this conjecture including, for example, the product space $T^2\times S^2$. Following the first appearance of our counterexample on the arXiv Ghys put forward a revised conjecture, which predicts only the existence of a nilpotent normal subgroup of index at most n(M). Our main result is the proof of the revised Ghys conjecture. More generally, we show that the same result holds for homeomorphism groups of not necessarily compact topological manifolds with finitely generated homology groups. Our proofs are based on finite group theoretic results which provide a general strategy for proving similar Jordan-type theorems.
