Aspects of Non-positively Curved Groups

非正曲群的方面

• 批准号: 418456-2012
• 负责人: MartinezPedroza, Eduardo
• 金额: $ 1.24万
• 依托单位: Memorial University of Newfoundland
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2017
• 资助国家: 加拿大
• 起止时间: 2017-01-01 至 2018-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=635485
• 关键词: Aspects; Non; positively; Curved; Groups

Group theory is the area of mathematics that uses algebraic methods to abstract the idea of symmetry. A square has 8 distinct symmetries consisting of 4 rotations and 4 reflections. In contrast, there are objects with infinitely many symmetries as the tiling of the Euclidean plane by squares. The study of groups of symmetries have had applications to diverse areas of science like cosmology, cryptography, or robotics. The research proposal deals with the study of infinite groups of symmetries. The program is part of the difficult problem of classifying and understanding the structure of this class of groups. The investigator will explore the use of specific combinatorial notions of curvature on topological complexes to study the structure of discrete groups acting on them. This involves the use of sophisticated techniques belonging to the areas of algebraic topology, hyperbolic geometry, and combinatorial group theory. The proposal can be classified in the general area of geometric group theory. The outcome of this research program will improve our understanding of the connection between geometric and algebraic properties of infinite discrete groups, and will shed some light on outstanding open problems in geometric group theory. The research program contains a training aspect which outlines research projects at the undergraduate and postgraduate levels. These projects aim to produce highly qualified personnel in the areas of low dimensional topology and geometric group theory.

小组理论是使用代数方法来抽象对称性的数学领域。一个正方形具有8个不同的对称性，由4个旋转和4个反射组成。相比之下，有许多对称对称性的物体作为正方形的欧几里得平面的瓷砖。对对称性组的研究已应用于宇宙学，密码学或机器人技术等科学领域。该研究建议涉及无限对称组的研究。该程序是对这类组的结构进行分类和理解的困难问题的一部分。研究者将探讨曲率在拓扑复合物上使用特定的组合概念来研究作用于它们的离散组的结构。这涉及使用属于代数拓扑，双曲线几何和组合群理论领域的复杂技术。该建议可以分类为几何群体理论的一般领域。该研究计划的结果将提高我们对无限离散群体几何和代数特性之间的联系的理解，并将对几何组理论中的出色开放问题有所了解。该研究计划包含一个培训方面，概述了本科和研究生级别的研究项目。这些项目旨在在低维拓扑和几何群体理论领域中产生高素质的人员。