论文标题
扭转同源性增长和廉价重建内在群体
Torsion homology growth and cheap rebuilding of inner-amenable groups
论文作者
论文摘要
我们证明，实际上无扭转的，有限的群体是内部不可且不可弥补的，具有便宜的1个建造属性，这是Abért，Bergeron，Frączyk和Gaboriau最近引入的概念。结果，这些组的第一个$ \ ell^2 $ -betti编号具有任意字段系数和1度的对数转换。这扩展了先前针对内部符合的组已知的结果。我们使用Tucker-Drob的结构定理，以表明存在Q-正常亚组链的内部成群。
We prove that virtually torsion-free, residually finite groups that are inner-amenable and non-amenable have the cheap 1-rebuilding property, a notion recently introduced by Abért, Bergeron, Frączyk and Gaboriau. As a consequence, the first $\ell^2$-Betti number with arbitrary field coefficients and log-torsion in degree 1 vanish for these groups. This extends results previously known for amenable groups to inner-amenable groups. We use a structure theorem of Tucker-Drob for inner-amenable groups showing the existence of a chain of q-normal subgroups.
