论文标题
[IA_N，IA_N]和Johnson内核有效的有限生成
Effective finite generation for [IA_n,IA_n] and the Johnson kernel
论文作者
论文摘要
令$ ia_n $表示$ ia $ - $ n $的$ ia $ - automormormormorphisms，然后让$ \ Mathcal i_n^b $表示$ n $的可定向表面的映射类群体的Torelli子组，带有$ n $，带有$ b $ b $ bugh bounceentents，$ b = 0,1,1 $。 1935年，马格努斯（Magnus）证明了$ ia_n $均为所有$ n $有限生成，1983年，约翰逊证明，$ \ Mathcal i_n^b $有限地生成$ n \ geq 3 $。 最近显示的是，对于\ Mathbb n $中的每个$ k \，$ k^{\ rm th} $ perther central系列$γ_kia_n $和$γ_k\ nathcal i_n^b $在$ n >> k $时有限地生成；但是，没有以$ k> 1 $闻名的有限生成集的信息。本文的主要目的是为$γ_2ia_n = [ia_n，ia_n] $构建一个明确的有限生成集，几乎明确的有限生成套件，用于$γ_2\ Mathcal I_n^b $和Johnson Kernel，其中包含$γ_2\ Mathcal I_n^b $ nime nime Indite Indite Indite。
Let $IA_n$ denote the group of $IA$-automorphisms of a free group of rank $n$, and let $\mathcal I_n^b$ denote the Torelli subgroup of the mapping class group of an orientable surface of genus $n$ with $b$ boundary components, $b=0,1$. In 1935 Magnus proved that $IA_n$ is finitely generated for all $n$, and in 1983 Johnson proved that $\mathcal I_n^b$ is finitely generated for $n\geq 3$. It was recently shown that for each $k\in\mathbb N$, the $k^{\rm th}$ terms of the lower central series $γ_k IA_n$ and $γ_k\mathcal I_n^b$ are finitely generated when $n>>k$; however, no information about finite generating sets was known for $k>1$. The main goal of this paper is to construct an explicit finite generating set for $γ_2 IA_n = [IA_n,IA_n]$ and almost explicit finite generating sets for $γ_2\mathcal I_n^b$ and the Johnson kernel, which contains $γ_2\mathcal I_n^b$ as a finite index subgroup.
