Obstructions to positive curvature and symmetry

正曲率和对称性的障碍

基本信息

批准号：
1622541
负责人：
Lee Kennard
金额：
$ 4.73万
依托单位：
University of Oklahoma Norman Campus
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2015
资助国家：
美国
起止时间：
2015-10-15 至 2017-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1622541&HistoricalAwards=false
关键词：
Obstructions positive curvature symmetry

项目摘要

AbstractAward: DMS 1404670, Principal Investigator: Lee Kennard, Guofang WeiThe curvature of a manifold is an attempt to quantify the ways that a space may bend, beginning with the Euclidean plane, whose flatness is captured by declaring the plane to have zero curvature. The two-dimensional round sphere in three-dimensional space has positive curvature, of a size that reflects the sense that as one traverses a sphere of large radius, its tangent plane turns more slowly in space than the tangent plane to a sphere of smaller radius: the sphere of radius R has curvature 1/R^2. Manifolds of curvature greater than or equal to zero have been an active area of study for many years, with most known examples produced by imposing some amount of symmetry, with the sphere and its large group of rotations being the most symmetric example.These research projects bring homotopy-theoretic tools into the approach of Grove and Ziller to the study of Riemannian manifolds of non-negative curvature. Some of the questions to be studied follow on well-known theorems and conjectures of Adem, Adams, and Chern. In particular, a generalization is suggested of Adams' theorem on singly-generated cohomology rings and generalizations in the presence of symmetry for Chern's problem on the fundamental groups of positively curved manifolds are considered.

Abstractaward：DMS 1404670，主要研究人员：lee Kennard，Guofang Weithe curvature a Prisold的曲率是一种尝试量化空间可能弯曲的方式，从欧几里得平面开始，其平坦度是通过宣布平面为零曲率的稳定性。三维空间中的二维圆形球体具有正曲率，其大小反映了一种感觉，即当一个人穿越较大半径的球体时，其切线平面在空间中的变化比切线平面慢于较小半径的球体：半径r的球体r radius r的球体具有曲率1/r^2。 Manifolds of curvature greater than or equal to zero have been an active area of study for many years, with most known examples produced by imposing some amount of symmetry, with the sphere and its large group of rotations being the most symmetric example.These research projects bring homotopy-theoretic tools into the approach of Grove and Ziller to the study of Riemannian manifolds of non-negative curvature. 众所周知的定理和Adem，Adams和Chern的猜想遵循的一些问题。特别是，考虑到在存在对称性的对称性问题上，在Chern在存在对称性的情况下，考虑了Adams对单一生成的共同体学环和概括的概括。