论文标题
绘制属$ \ geq 3 $表面的类群组组几乎不会过渡到$ \ mathbb {z} $
Mapping class groups of surfaces of genus $\geq 3$ do not virtually surject to $\mathbb{Z}$
论文作者
论文摘要
We prove a well known conjecture of Nikolai Ivanov which states that if $X$ is a surface of genus $\geq 3$ (with any number of punctures and boundary components), $\rm{Mod}(X)$ is the mapping class group of $X$, and $K < \rm{Mod}(X)$ is a finite-index subgroup, then $K$ does not virtually surject to $ \ mathbb {z} $。作为推论，我们会得到$ h_1（z; \ m athbb {q}）= 0 $，每当$ z $都是$ \ mathcal {m} _ {m} _ {g，n} $的有限盖，这是$ g \ geq 3 $ n $ n $标记点的复杂代数曲线的模态空间。
We prove a well known conjecture of Nikolai Ivanov which states that if $X$ is a surface of genus $\geq 3$ (with any number of punctures and boundary components), $\rm{Mod}(X)$ is the mapping class group of $X$, and $K < \rm{Mod}(X)$ is a finite-index subgroup, then $K$ does not virtually surject to $\mathbb{Z}$. As a corollary of this we get that $H_1(Z; \mathbb{Q}) = 0$ whenever $Z$ is a finite cover of $\mathcal{M}_{g,n}$, the moduli space of complex algebraic curves of genus $g\geq 3$ with $n$ marked points.
