Coarse Geometry of Groups and Spaces

群和空间的粗略几何

• 批准号: 2766916
• 金额: --
• 依托单位: University of Bristol
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2766916
• 关键词: Coarse; Geometry; Groups; Spaces

Monotone Coarse Invariants (MCIs) are POset valued Coarse-invariants of metric spaceswhich behave monotonically with respect to Coarse embeddings i.e if X coarsely em-beds in Y the invariants for X and Y , say fX and fY satisfy fX fY . Classical examplesinclude Growth and Asymptotic Dimension. MCIs allow us to create obstructions toCoarse embeddings. In the last ten years, the number and diversity of MCIs have in-creased dramatically, with new MCIs inspired by techniques from combinatorics, anal-ysis, topology, electrical network theory, and neural networks. The goal of the projectis to further develop these MCIs as tools to tackle key problems in geometric grouptheory, fractal geometry, and beyond. This project falls under the EPSRC research theme 'Mathematical Sciences'.

单调粗不变量(MCI)是度量空间中关于粗嵌入单调表现的集值粗不变量，即如果X粗嵌入Y，则X和Y的不变量，比如FX和FY满足FX，FY。经典的例子包括增长和渐近维度。MCI允许我们设置障碍物，以降低嵌入的难度。在过去的十年里，MCIS的数量和多样性急剧增加，受到组合学、分析、拓扑学、电网络理论和神经网络技术的启发，出现了新的MCIS。该项目的目标是进一步开发这些MCIS，将其作为工具来解决几何群论、分形几何等领域的关键问题。该项目属于EPSRC的研究主题“数学科学”。