论文标题
强大的拓扑rokhlin属性，阴影和可数组的符号动态
Strong topological Rokhlin property, shadowing, and symbolic dynamics of countable groups
论文作者
论文摘要
一个可数的$ g $具有强大的拓扑rokhlin物业（STRP），如果它承认与稳定的共轭类对坎托空间的连续行动。我们表明，具有strp是符号动力学属性。我们证明，当且仅当某些超过$ g $以上的sofic subshift在subshifts的空间中，且只有某些SOFIC子换档在$ g $上的某些sofic shifts时，我们就证明了一个可数的$ g $。一个充分的条件是，在所有滑移的空间中，超过$ g $的孤立偏移是密集的。 我们提供了许多应用程序，包括证据表明，将有限或环状群体的自由产品分解为strp。我们表明，除非它们实际上是循环的，否则有限生成的nilpotent组没有STRP。对于$ g_1 \ times g_2 \ times g_3 $的许多组的许多组也是如此，其中每个因子都会递归呈现。我们表明，一大批非最终生成的组没有STRP，其中包括任何具有无限生成中心的组和Hall Universal在本地有限的组。 我们发现strp和阴影之间的连接非常牢固，又称伪轨追踪属性。我们表明，当$ g $具有strp时，阴影对于有限生成的组$ g $的动作是通用的。
A countable group $G$ has the strong topological Rokhlin property (STRP) if it admits a continuous action on the Cantor space with a comeager conjugacy class. We show that having the STRP is a symbolic dynamical property. We prove that a countable group $G$ has the STRP if and only if certain sofic subshifts over $G$ are dense in the space of subshifts. A sufficient condition is that isolated shifts over $G$ are dense in the space of all subshifts. We provide numerous applications including the proof that a group that decomposes as a free product of finite or cyclic groups has the STRP. We show that finitely generated nilpotent groups do not have the STRP unless they are virtually cyclic; the same is true for many groups of the form $G_1\times G_2\times G_3$ where each factor is recursively presented. We show that a large class of non-finitely generated groups do not have the STRP, this includes any group with infinitely generated center and the Hall universal locally finite group. We find a very strong connection between the STRP and shadowing, a.k.a. pseudo-orbit tracing property. We show that shadowing is generic for actions of a finitely generated group $G$ if and only if $G$ has the STRP.
