Compactifications and Local-to-Global Structure for Bruhat-Tits Buildings

Bruhat-Tits 建筑的紧凑化和局部到全局结构

• 批准号: 336349957
• 负责人: Professor Dr. Linus Kramer
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Priority Programmes
• 财政年份: 2017
• 资助国家: 德国
• 起止时间: 2016-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/336349957?language=en
• 关键词: Compactifications; Local; Global; Structure; Bruhat

We plan to study compactifications and local-global principles of Bruhat-Tits buildings. The compactifications will be constructed as horofunction completions, starting with asymmetric polyhedral norms on the maximal flats of the building. The ultimate goal is to study the dynamics of discrete group actions on the buildings. Our methods use ultraproducts, topolgical vector spaces and CAT(0) geometry.For the local-global principles we plan to study metric balls in the Chamber graphs of Bruhat-Tits buildings. Recent results for a special class of Bruhat-Tits buildings indicate that there is an interesting dichotomy between the case of function fields and p-adic fields, which we want to explore from a geometric viewpoint.

我们计划研究Bruhat-Tits建筑的紧致化和局部-全局原则。紧化将被构造为时函数完备化，从建筑物的最大平面上的非对称多面体范数开始。 最终目标是研究离散群体对建筑物的作用动力学。我们的方法使用了超积、拓扑向量空间和CAT（0）几何，对于局部-整体原理，我们计划研究Bruhat-Tits建筑的Chamber图中的度量球.最近的结果一类特殊的Bruhat-Tits建筑物表明，有一个有趣的二分法之间的情况下，功能领域和p-adic领域，我们要探讨从几何的观点。