论文标题
关于曾经启动的圆环束的角色品种的拓扑
On the topology of character varieties of once-punctured torus bundles
论文作者
论文摘要
本文介绍了曾经启动的圆环束的特殊情况，这是一种自然方法，是研究圆环的双曲线3个manifolds的特征品种。主要策略是将字符限制为束的光纤，并分析所得的分支覆盖地图。这使我们能够扩展史蒂文·博耶（Steven Boyer），埃尔哈德·卢夫特（Erhard Luft）和Xingru Zhang的结果。 $ sl（2，\ mathbb {c}）$ - 字符品种和$ psl（2，\ mathbb {c}）$ - 字符品种。作为这些方法的明确应用，我们以贝克和彼得森的作品为基础，以表明有一个无限的双曲线曾经是曾经的捆绑捆绑包，其规范曲线为$ psl（2，\ m athbb {c}）$ - 无界属的字符。
This paper presents, for the special case of once-punctured torus bundles, a natural method to study the character varieties of hyperbolic 3-manifolds that are bundles over the circle. The main strategy is to restrict characters to the fibre of the bundle, and to analyse the resulting branched covering map. This allows us to extend results of Steven Boyer, Erhard Luft and Xingru Zhang. Both $SL(2, \mathbb{C})$-character varieties and $PSL(2, \mathbb{C})$-character varieties are considered. As an explicit application of these methods, we build on work of Baker and Petersen to show that there is an infinite family of hyperbolic once-punctured bundles with canonical curves of $PSL(2, \mathbb{C})$-characters of unbounded genus.
