论文标题
Putman-Wieland猜想的代数几何形状的应用
Applications of the algebraic geometry of the Putman-Wieland conjecture
论文作者
论文摘要
我们向Putman-Wieland的猜想提供了两项先前工作的申请。首先，我们推断了马尔可维奇·托斯（Marković-Tošić）在虚拟映射封面同源性的班级组合中的结果。其次，令$ g \ geq 2 $，让$σ_{g'，n'} \ toσ_{g，n} $为有限的$ h $ - 拓扑表面。我们在$ h $ - 异型组件上显示了$ h^1（σ_{g'}）$的$σ_{g，n+1} $的映射类组的虚拟动作。
We give two applications of our prior work toward the Putman-Wieland conjecture. First, we deduce a strengthening of a result of Marković-Tošić on virtual mapping class group actions on the homology of covers. Second, let $g\geq 2$ and let $Σ_{g',n'}\to Σ_{g, n}$ be a finite $H$-cover of topological surfaces. We show the virtual action of the mapping class group of $Σ_{g,n+1}$ on an $H$-isotypic component of $H^1(Σ_{g'})$ has non-unitary image.
