The large scale geometry of strongly aperiodic subshifts of finite type
The large scale geometry of strongly aperiodic subshifts of finite type
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有限型强非周期子移的大尺度几何
DOI：
10.1016/j.aim.2016.12.016
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
D. Cohen
中科院分区：
文献类型：
--
作者：
D. Cohen
群G上的子移位是群G的闭G-不变子集，对于某个有限集A。如果G中的所有点稳定子都是平凡的，则它是强非周期的;如果G中的所有点稳定子都是无穷指数的，则它是弱非周期的。我们表明，至少有2个结束的群体有一个强非周期性的SFT，并有这样的SFT是一个QI不变量的群。我们证明了一个不具有弱非周期SFT的无挠群是QI-刚性的。G上的多米诺骨牌问题询问由给定的一组禁止模式指定的SFT是否为空。我们证明了多米诺骨牌问题的可判定性是一个QI不变量。
A subshift on a group G is a closed, G-invariant subset of A G, for some finite set A. It is said to be a subshift of finite type (SFT) if it is defined by a finite collection of “forbidden patterns”, to be strongly aperiodic if all point stabilizers are trivial, and weakly aperiodic if all point stabilizers are infinite index in G. We show that groups with at least 2 ends have a strongly aperiodic SFT, and that having such an SFT is a QI invariant for finitely presented groups. We show that a finitely presented torsion free group with no weakly aperiodic SFT must be QI-rigid. The domino problem on G asks whether the SFT specified by a given set of forbidden patterns is empty. We show that decidability of the domino problem is a QI invariant.