Algebraic and arithmetic aspects of aperiodicity (A02)

非周期性的代数和算术方面（A02）

• 批准号: 517382981
• 金额: --
• 依托单位: Fachgebiet Computeralgebra und Zahlentheorie
• 依托单位国家: 德国
• 项目类别: CRC/Transregios
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/517382981?language=en
• 关键词: Algebraic; arithmetic; aspects; aperiodicity; A02

This project aims at the analysis and classification of certain topological dynamical systems of geometric and number-theoretic origin. In particular, the systems induced by k-free integers in orders of algebraic number fields will be investigated via their generalised symmetries, their topological entropy and other number-theoretic invariants. Further, inflation tiling systems will be analysed topologically by extensions of existing cohomological tools towards profinite fundamental groups of tiling spaces.

本项目旨在分析和分类某些几何和数论起源的拓扑动力系统。特别地，我们将通过广义对称性、拓扑熵和其他数论不变量来研究由k-自由整数在数论数论域中诱导的系统。此外，膨胀平铺系统将通过扩展现有的上同调工具对平铺空间的无限基本群进行拓扑分析。