论文标题
映射课程组的刚度曲折的力量
Rigidity of mapping class groups mod powers of twists
论文作者
论文摘要
我们研究了通过合适的Dehn Twist的绘制刺穿球体的绘制阶级组的商，显示了伊万诺夫定理的类似物，以曲线图的相应商的自动形态学。然后，我们使用此结果来证明这些商的准时刚度，在刺破球体的情况下回答了Behrstock，Hagen，Martin和Sisto的问题。最后，我们表明，我们的映射课程组的自动形态群体和他们的抽象同源器都是“小”的。这再次是伊万诺夫定理的类似物，内容涉及映射类组的自动形态组。在此过程中，我们开发了从分层双曲线空间的准静电法中提取组合数据的技术，并使用它们来给出了鲍迪奇的结果，以证明鲍迪奇的结果是裤子的裤子图形图。
We study quotients of mapping class groups of punctured spheres by suitable large powers of Dehn twists, showing an analogue of Ivanov's theorem for the automorphisms of the corresponding quotients of curve graphs. Then we use this result to prove quasi-isometric rigidity of these quotients, answering a question of Behrstock, Hagen, Martin, and Sisto in the case of punctured spheres. Finally, we show that the automorphism groups of our quotients of mapping class groups are "small", as are their abstract commensurators. This is again an analogue of a theorem of Ivanov about the automorphism group of the mapping class group. In the process we develop techniques to extract combinatorial data from a quasi-isometry of a hierarchically hyperbolic space, and use them to give a different proof of a result of Bowditch about quasi-isometric rigidity of pants graphs of punctured spheres.
