The large scale geometry of strongly aperiodic subshifts of finite type

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• 作者：David Bruce Cohen ^{davidbrucecohen@gmail.com}
• 关键词：Geometric group theory ; Symbolic dynamics
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：21 February 2017
• 年：2017
• 卷：308
• 期：Complete
• 页码：599-626
• 全文大小：546 K
• 卷排序：308

文摘

A subshift on a group G is a closed, G  -invariant subset of AGAG, 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.