论文标题
映射课程组，多个Kodaira纤维和CAT（0）空间
Mapping class groups, multiple Kodaira fibrations, and CAT(0) spaces
论文作者
论文摘要
我们研究了与Kodaira纤维相关的几种几何和组理论问题，用于较大的Riemann表面家族以及逐个表面组。首先，我们对Kodaira纤维的限制以多种不同的方式纤维纤维，解决了Catanese和Salter关于其存在的问题。然后，我们表明，如果表面上的表面束的基本组为$ {\ rm cat}（0）$组，则捆绑包必须具有注入性的单片（除非单片构造具有有限的图像）。最后，鉴于一个封闭的Riemann表面（属$ \ ge 2 $）的一系列带有注入性的单型$ e \ to B $上的b $上的b $，我们解释了如何建立一个新的Riemann表面，其基本底座的基础是总空间$ e $ e $，其纤维具有更高的属，其基础是较高的属。我们运用我们的构造来证明，曾经刺穿的表面的映射类别几乎可以接收到较高属的封闭表面的映射类组。
We study several geometric and group theoretical problems related to Kodaira fibrations, to more general families of Riemann surfaces, and to surface-by-surface groups. First we provide constraints on Kodaira fibrations that fiber in more than two distinct ways, addressing a question by Catanese and Salter about their existence. Then we show that if the fundamental group of a surface bundle over a surface is a ${\rm CAT}(0)$ group, the bundle must have injective monodromy (unless the monodromy has finite image). Finally, given a family of closed Riemann surfaces (of genus $\ge 2$) with injective monodromy $E\to B$ over a manifold $B$, we explain how to build a new family of Riemann surfaces with injective monodromy whose base is a finite cover of the total space $E$ and whose fibers have higher genus. We apply our construction to prove that the mapping class group of a once punctured surface virtually admits injective and irreducible morphisms into the mapping class group of a closed surface of higher genus.
