Topics at the Intersection of Geometry, Topology and Group Theory
几何、拓扑和群论交叉的主题
基本信息
- 批准号:0604633
- 负责人:
- 金额:$ 33.36万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Continuing Grant
- 财政年份:2006
- 资助国家:美国
- 起止时间:2006-07-01 至 2012-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
ABSTRACT FOR NSF PROPOSAL 0604633There are three main components to this project. First, Farb will continue to investigate mapping class groups and the moduli space of Riemann surfaces. This topic lies at the intersection of many areas of mathematics, from algebraic geometry to low-dimensional topology to string theory to geometric group theory. Farb will continue to apply methods from discrete subgroups of Lie groups in order to understand these objects, especially the "Torelli group", which is a part of the oldest but least understood part of the theory. Symmetry is a core idea in mathematics. Farb will continue his work with S. Weinberger on the broad program of classifying all spaces (that is Riemannian manifolds) with symmetry. The ideas used so far in this work have included the theories of harmonic maps, large-scale geometry, and transformation groups. In a third project, Farb will continue his work with C. Hruska on bringing together techniques and ideas from geometric group theory with those from discrete subgroups of Lie groups in order to build the theory of lattices in automorphism groups of 2-complexes. This is a 2-dimensional extension of Bass-Lubotzky's theory of tree lattices, where wild new phenomena can occur. Throughout each of the projects just described, Farb will continue to work with and mentor many young students and researchers.
NSF提案0604633摘要本项目有三个主要组成部分。 首先,法布将继续调查映射类组和模空间的黎曼曲面。 这个主题是在许多数学领域的交叉点,从代数几何到低维拓扑学到弦论到几何群论。 法布将继续适用的方法,从离散子群的李群,以了解这些对象,特别是“Torelli组”,这是一个部分的最古老的,但最不了解的一部分理论。 对称性是数学的核心思想。 法布将继续他的工作与S。Weinberger对所有空间(即黎曼流形)进行对称性分类的广泛计划。 到目前为止,在这项工作中使用的思想包括调和映射,大规模几何和变换群的理论。 在第三个项目中,Farb将继续他与C的工作。Hruska汇集的技术和思想,从几何群论与那些从离散子群的李群,以建立理论的格自同构群的2-复合物。 这是巴斯-卢博茨基的树格理论的二维扩展,在树格中可以出现狂野的新现象。在刚刚描述的每个项目中,Farb将继续与许多年轻学生和研究人员合作并指导他们。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Benson Farb其他文献
Every mapping class group is generated by 3 elements of finite order
每个映射类组由3个有限阶元素生成
- DOI:
- 发表时间:
2003 - 期刊:
- 影响因子:0
- 作者:
Tara E. Brendle;Benson Farb - 通讯作者:
Benson Farb
Combing Lattices in Semisimple Lie Groups
组合半单李群中的格
- DOI:
10.1515/9783110908978.57 - 发表时间:
1995 - 期刊:
- 影响因子:0
- 作者:
Benson Farb - 通讯作者:
Benson Farb
Filling-invariants at infinity for manifolds of nonpositive curvature
非正曲率流形的无穷远填充不变量
- DOI:
- 发表时间:
1995 - 期刊:
- 影响因子:0
- 作者:
N. Brady;Benson Farb - 通讯作者:
Benson Farb
Geometry of the Wiman–Edge pencil and the Wiman curve
维曼边缘铅笔的几何形状和维曼曲线
- DOI:
10.1007/s10711-020-00517-7 - 发表时间:
2019-12 - 期刊:
- 影响因子:0.5
- 作者:
Igor Dolgachev;Benson Farb;Eduard Looijenga - 通讯作者:
Eduard Looijenga
Some problems on mapping class groups and moduli space
- DOI:
10.1090/pspum/074/2264130 - 发表时间:
2006-06 - 期刊:
- 影响因子:0
- 作者:
Benson Farb - 通讯作者:
Benson Farb
Benson Farb的其他文献
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{{ truncateString('Benson Farb', 18)}}的其他基金
New Directions in Geometric Group Theory and Topology
几何群论和拓扑学的新方向
- 批准号:
2203355 - 财政年份:2022
- 资助金额:
$ 33.36万 - 项目类别:
Continuing Grant
Braids, Resolvent Degree and Hilbert's 13th Problem
辫子、解决度和希尔伯特第十三问题
- 批准号:
1811772 - 财政年份:2018
- 资助金额:
$ 33.36万 - 项目类别:
Continuing Grant
Stability and Instability in Topology
拓扑的稳定性和不稳定性
- 批准号:
1406209 - 财政年份:2014
- 资助金额:
$ 33.36万 - 项目类别:
Continuing Grant
Representation Theory and Homological Stability in Topology
拓扑中的表示论和同调稳定性
- 批准号:
1105643 - 财政年份:2011
- 资助金额:
$ 33.36万 - 项目类别:
Continuing Grant
Geometry and Dynamics of the group of Hamiltonian diffeomorphisms of a surface
表面哈密顿微分同胚群的几何与动力学
- 批准号:
0905911 - 财政年份:2009
- 资助金额:
$ 33.36万 - 项目类别:
Standard Grant
Geometry, Rigidity, and Group Actions
几何、刚度和群作用
- 批准号:
0734851 - 财政年份:2007
- 资助金额:
$ 33.36万 - 项目类别:
Standard Grant
CAREER: Topics at the Intersection of Geometry, Topology and Group Theory
职业:几何、拓扑和群论交叉的主题
- 批准号:
9984815 - 财政年份:2000
- 资助金额:
$ 33.36万 - 项目类别:
Standard Grant
Large Scale Geometry, Topology, and Rigidity in Geometric Group Theory
几何群论中的大尺度几何、拓扑和刚性
- 批准号:
9704640 - 财政年份:1997
- 资助金额:
$ 33.36万 - 项目类别:
Standard Grant
Mathematical Sciences: Postdoctoral Research Fellowship
数学科学:博士后研究奖学金
- 批准号:
9407555 - 财政年份:1994
- 资助金额:
$ 33.36万 - 项目类别:
Fellowship Award
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