论文标题
群体上的自动不动数形成组
Aut-invariant quasimorphisms on groups
论文作者
论文摘要
对于一大批群体，我们表现出在自多态群体的作用下不变的均质准晶体的无限尺寸空间。该类包括非元素双曲线组，无限限制的有限生成的组，一些相对双曲线的组以及一类组的图形产品，包括所有几乎不是Abelian的所有直角Artin和Coxeter组。这是由Brandenbursky和Marcinkowski的结果以$ F_2 $而闻名的，但即使是自由排名的自由团体，也是新的，也解决了MiklósAbért的问题。有限生成的阿贝尔团体的图形产品解决了Michal Marcinkowski的问题。结果，我们推断出此类群体的各种自动不动数规范是无限的。
For a large class of groups, we exhibit an infinite-dimensional space of homogeneous quasimorphisms that are invariant under the action of the automorphism group. This class includes non-elementary hyperbolic groups, infinitely-ended finitely generated groups, some relatively hyperbolic groups, and a class of graph products of groups that includes all right-angled Artin and Coxeter groups that are not virtually abelian. This was known for $F_2$ by a result of Brandenbursky and Marcinkowski, but is new even for free groups of higher rank, settling a question of Miklós Abért. The case of graph products of finitely generated abelian groups settles a question of Michal Marcinkowski. As a consequence, we deduce that a variety of Aut-invariant norms on such groups are unbounded.
