NSF/CBMS Regional Conference in the Mathematical Sciences -Non-Positive Curvature in Group Theory; Albany, NY; August 15-20, 2004

NSF/CBMS 数学科学区域会议 - 群论中的非正曲率；

• 批准号: 0333532
• 负责人: Edward Turner
• 金额: $ 3.2万
• 依托单位: SUNY at Albany
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-08-01 至 2005-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0333532&HistoricalAwards=false
• 关键词: NSF; CBMS; Regional; Conference; Mathematical

We begin with a discussion of the origins of geometric group theory: the importance of the core decision problems first formulated by Dehn; the emergence of classes of groups that demand special attention; and the emergence of negative and non-positive curvature from the core issues in group theory. This leads to a description of the geography of the universe of finitely presented groups, with emphasis on the role played by manifestations of non-positive curvature.From this platform, the following topics will be developed.The study and construction of group actions; complexes of groups, the role of non-positive curvature indevlopability. The fundamental groups of non-positively curved (orbi)spaces. Rigidity. Concepts of dimension.Hyperbolic groups. Towards semihyperbolic groups: competing theories and the difficulties of discriminating between the associated classes of groups. The rich and diverse subgroup theory.Algorithmic structures: connecting the complexity of the basic decision problems to the geometry of manifolds via diagrams; Dehn functions and the isoperimetric spectrum; language-theoretic complexity, the geometry of normal forms, automatic groups.Conjugacy problems and cryptography.Isomorphism problems for groups and manifolds in the presence of non-positive curvature (positive and negative results).Throughout, many examples will be given to complement the elegance of the general theory and to illustrate how ideas from non-positive curvature in group theory can be applied elsewhere, eg the solution to Grothendieck's problems concerning profinite completions.

我们首先讨论了几何群体理论的起源：Dehn首先提出的核心决策问题的重要性；需要特别关注的群体类别的出现；以及群体理论中核心问题的负和非阳性曲率的出现。这导致了对有限呈现的群体宇宙宇宙的描述，重点是非阳性曲率表现所起的作用。从这个平台开始，将开发以下主题。小组行动的研究和构建；组的复合物，非阳性曲率不忽视性的作用。非物性弯曲（ORBI）空间的基本组。刚性。尺寸的概念。遗传基团。迈向半节日群：竞争理论和在相关群体之间区分群体的困难。富裕而多样化的亚组理论。烯烃结构：将基本决策问题的复杂性与通过图的流形的几何形状联系起来； DEHN功能和等值光谱；语言理论的复杂性，正常形式的几何形状，自动组。结合性问题和密码学。在存在非阳性曲率的情况下的群体和流形问题（积极和负面结果）。将给出许多例子，许多例子将提供许多示例，以补充一般理论的依据，以补充整体理论的优雅理论。完善的完成。