论文标题
右角ARTIN组作为映射课程组的正常亚组
Right-angled Artin groups as normal subgroups of mapping class groups
论文作者
论文摘要
我们构建了与非无右角artin组同构的映射类组的正常亚组的第一个示例。我们的建筑还提供了其他组的正常，非右角的Artin子组，例如编织组和纯编织组，以及映射类组的许多亚组，例如Torelli亚组。我们的工作恢复并概括了大曼尼 - 吉拉德尔 - 酪氨酸的开创性结果，该结果给出了映射类基团的免费，纯粹的伪-Anosov正常亚组。我们提供了两种方法的应用：（1）我们制作了映射类组的明确适当的正常子组，在任何级别的$ m $一致性子组中都不包含，（2）我们提供了一个明确的示例示例，该典范与伪anosov映射类别与其所有属性的属性，所有这些属性都可以自由地封闭，并且是自由的正常封闭，并正常派出了整个型号的组合组。我们作品核心的技术定理是Dahmani-Guirardel-Osin的Windmill设备的新版本，该设备是针对Bestvina-Bromberg-Fujiwara投射综合体的集体动作量身定制的。
We construct the first examples of normal subgroups of mapping class groups that are isomorphic to non-free right-angled Artin groups. Our construction also gives normal, non-free right-angled Artin subgroups of other groups, such as braid groups and pure braid groups, as well as many subgroups of the mapping class group, such as the Torelli subgroup. Our work recovers and generalizes the seminal result of Dahmani-Guirardel-Osin, which gives free, purely pseudo-Anosov normal subgroups of mapping class groups. We give two applications of our methods: (1) we produce an explicit proper normal subgroup of the mapping class group that is not contained in any level $m$ congruence subgroup, and (2) we produce an explicit example of a pseudo-Anosov mapping class with the property that all of its even powers have free normal closure and its odd powers normally generate the entire mapping class group. The technical theorem at the heart of our work is a new version of the windmill apparatus of Dahmani-Guirardel-Osin, which is tailored to the setting of group actions on the projection complexes of Bestvina-Bromberg-Fujiwara.
