Cohomology, curvature, classifying spaces and symmetry

上同调、曲率、空间分类和对称性

• 批准号: 0804226
• 负责人: Ian Leary
• 金额: $ 12.59万
• 依托单位: Ohio State University Research Foundation -DO NOT USE
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2008
• 资助国家: 美国
• 起止时间: 2008-07-15 至 2011-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0804226&HistoricalAwards=false
• 关键词: Cohomology; curvature; classifying; spaces; symmetry

Professor Leary will continue research on geometric group theory, and geometric topology, both alone and in collaboration. In particular, he will construct infinite groups having strong fixed point properties. This is expected to have application to the study of Kropholler's hierarchy of groups. He will also study a functor that he has developed (from simplicial complexes to locally CAT(0) cubicalcomplexes) that preserves homology. This work should have applications to topology, K-theory and group theory. He will also classify all spaces that can be built by gluing polygons in a certain way that have the `largest possible' groups of symmetries.A group is the mathematician's abstraction of the notion of symmetry:groups measure symmetry in the same way that numbers measure quantity.There are fascinating connections between group theory and geometry.Professor Leary aims to construct groups with surprising combinations of properties, which should lead to new results and insights within both geometry and group theory. He will also classify a family of geometrical objects which generalize the platonic solids, five symmetrical shapes that have been studied for at least four thousand years.

Leary教授将继续研究几何群论和几何拓扑，无论是单独还是合作。 特别是，他将建设无限群具有强大的不动点性质。 这是预期有应用程序的研究克罗福勒的层次结构的群体。 他还将研究一个函子，他已经开发（从单纯复体到局部CAT（0）marticalcomplex），保持同源性。 这项工作应具有应用拓扑结构，K-理论和群论。 他还将分类所有的空间，可以建立胶合多边形在一定的方式，有'最大可能'组的对称性。一个组是数学家的抽象概念的对称性：团体措施的对称性，以同样的方式，数字测量数量。有迷人的联系之间的群论和几何。 他还将对一系列几何对象进行分类，这些几何对象概括了柏拉图固体，这五种对称形状已经被研究了至少4000年。