双曲群上的强非周期SFT:在哪里找到它们以及为什么我们喜欢它们
Strongly aperiodic SFTs on hyperbolic groups: where to find them and why we love them
摘要:
D. B.科恩角Goodman-Strauss等人的结论,并证明了双曲群允许“SA SFT”当且仅当它至多有一端。本文有两个不同的部分:第一个是一个对话,解释什么是SA SFT以及它们如何使用。在第二部分中,我试图解释进入证明的旧思想和新思想。在原始文件中的具体要求的参考,希望任何有兴趣的读者可以找到细节后,阅读本说明书更容易。
英文摘要:
D. B. Cohen, C. Goodman-Strauss, and the author proved that a hyperbolic group admits an "SA SFT" if and only if it has at most one end. This paper has two distinct parts: the first is a conversation explaining what an SA SFT is and how they may be of use. In the second part I attempt to explain both old and new ideas that go into the proof. References to specific claims in the original paper are given, with the hope that any interested reader may be able to find the details there more accessible after reading this exposition.
机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。