RUI: Biquotients, Cohomogeneity-One Manifolds, and Double Disk Bundles

RUI：双商、同质一流形和双盘丛

基本信息

批准号：
2105556
负责人：
Jason DeVito
金额：
$ 9.93万
依托单位：
University of Tennessee Martin
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2021
资助国家：
美国
起止时间：
2021-07-01 至 2024-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2105556&HistoricalAwards=false
关键词：
RUI Biquotients Cohomogeneity Manifolds Double

项目摘要

The Principal Investigator seeks to increase our understanding of mathematical shapes, called manifolds, which are of particular interest to both physicists and mathematicians. One important class of manifolds are those that are everywhere positively curved or flat. The term "positive curvature" refers to curving like a sphere; a very large sphere is approximately flat, and so has a small but positive curvature. On the other hand, a very small sphere has a very large curvature. This project will focus on these objects through international collaborations, as well as through undergraduate research projects.The PI's work is motivated by the recent breakthrough of Goette, Kerin, and Shankar on finding metrics of non-negative sectional curvature on so-called codimension one biquotient foliations. These spaces generalize the well known cohomogeneity one manifolds, and all have a decomposition as a union of two disk bundles glued together along their common boundary. The PI will work on developing a method of classifying such objects. This includes studying the classification of non-simply connected biquotients, as well as developing obstructions at the level of cohomology for a manifold to admit such a structure.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

首席研究者试图增加我们对数学形状的理解，称为流形，这对物理学家和数学家都特别感兴趣。一类重要的歧管是到处弯曲或平坦的歧管。 “正弯曲”一词是指像球一样弯曲。一个非常大的球体大约是平坦的，因此具有较小但正的曲率。另一方面，一个很小的球体具有非常大的曲率。该项目将通过国际合作以及本科研究项目重点关注这些对象。PI的工作是由Goette，Kerin和Shankar的最新突破引起的，目的是在所谓的Codimension Codimension上寻找非负分段曲率的指标。这些空间概括了一个众所周知的同构性一个流形，并且都将分解作为沿着共同边界粘合在一起的两个磁盘束的结合。 PI将致力于开发对此类对象进行分类的方法。这包括研究非简单连接的生物品质的分类，以及在共同体学水平上发展障碍物，以承认这种结构。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的审查标准来通过评估来获得支持的。