Research in Geometric Group theory: Artin groups and Automorphism Groups
几何群论研究:Artin群和自同构群
基本信息
- 批准号:0705396
- 负责人:
- 金额:$ 15.76万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2007
- 资助国家:美国
- 起止时间:2007-08-01 至 2012-07-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project has two main parts. The first concerns automorphism groups of right-angled Artin groups. Right-angled Artin groups are finitely presented groups whose only relators are commutators. They may be viewed as interpolating between free groups and free abelian groups. Thus, their (outer) automorphism groups interpolate between Out(F_n) and GL(n,Z) and provide a context for understanding the similarities and differences between these groups. The goal is to generalize techniques used in the study of automorphism groups of free groups---such as the construction of a contractible "outer space" with a proper Out(F_n) action - and use these techniques to study properties of automorphism groups of arbitrary right-angled Artin groups. The second part of the project concerns more general Artin groups associated to infinite Coxeter groups. The project will address a number of questions regarding the coarse geometry of these groups.Geometric group theory may be viewed as the study of symmetry groups of geometric objects. A particularly rich class of geometric objects are cubical complexes with nice local structure. These complexes serve as models for a variety of problems in robotics and have applications to other areas of mathematics. Right-angled Artin groups arise as groups of symmetries of certain cubical complexes. Moreover, the groups themselves have interesting symmetries known as automorphisms. This project will investigate properties of these groups, their automorphisms and the associated geometries. In addition to right-angled Artin groups, the project will study the large scale geometry of more general Artin groups. Some Artin groups, such as braid groups, are well understood and have important applications to topology, cryptography, and other fields. Other Artin groups are much more mysterious and some of the most fundamental problems in group theory, such as the "word" and "conjugacy" problems, remain unanswered for these groups. By studying their large scale geometry, the project aims to gain insight into some of these more mysterious groups.
该项目有两个主要部分。 第一个是直角Artin群的自同构群。 直角Artin群是唯一的关系子是平行子的平行表示群。 它们可以看作是自由群和自由阿贝尔群之间的插值。 因此,它们的(外)自同构群内插在Out(F_n)和GL(n,Z)之间,并为理解这些群之间的相似性和差异性提供了背景。 目的是推广研究自由群的自同构群所使用的技巧-例如构造一个具有适当Out(F_n)作用的可收缩“外层空间”-并利用这些技巧来研究任意直角Artin群的自同构群的性质。 该项目的第二部分涉及更一般的阿廷组与无限Coxeter组。 该项目将解决一些关于这些群的粗糙几何的问题。几何群论可以被看作是对几何对象的对称群的研究。 一类特别丰富的几何对象是具有良好局部结构的立方体复合体。 这些复合体可以作为机器人中各种问题的模型,并应用于其他数学领域。 直角阿廷群作为某些立方复形的对称群而出现。 此外,群本身具有有趣的对称性,称为自同构。 这个项目将研究这些群的性质,它们的自同构和相关的几何。 除了直角Artin组,该项目将研究更一般的Artin组的大规模几何。 一些阿廷群,如辫群,是很好理解的,并在拓扑学,密码学和其他领域有重要的应用。 其他阿廷集团是更加神秘和一些最基本的问题,在群论,如“字”和“共轭”的问题,仍然没有答案,为这些团体。 通过研究它们的大规模几何形状,该项目旨在深入了解其中一些更神秘的群体。
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)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Ruth Charney其他文献
Convexity of parabolic subgroups in Artin groups
Artin 群中抛物线子群的凸性
- DOI:
10.1112/blms/bdu077 - 发表时间:
2014 - 期刊:
- 影响因子:0.9
- 作者:
Ruth Charney;L. Paris - 通讯作者:
L. Paris
Finite K (π, 1)s for Artin Groups
Artin 群的有限 K (π, 1)s
- DOI:
- 发表时间:
1996 - 期刊:
- 影响因子:0
- 作者:
Ruth Charney;Michael W. Davis - 通讯作者:
Michael W. Davis
Reciprocity of growth functions of Coxeter groups
Coxeter 群增长函数的互易
- DOI:
10.1007/bf00150764 - 发表时间:
1991 - 期刊:
- 影响因子:0.5
- 作者:
Ruth Charney;Michael W. Davis - 通讯作者:
Michael W. Davis
Singular Metrics of Nonpositive Curvature on Branched Covers of Riemannian Manifolds
黎曼流形分支覆盖上非正曲率的奇异度量
- DOI:
- 发表时间:
1993 - 期刊:
- 影响因子:0
- 作者:
Ruth Charney;Michael W. Davis - 通讯作者:
Michael W. Davis
Ruth Charney的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Ruth Charney', 18)}}的其他基金
Automorphism Groups and Morse Boundaries
自同构群和莫尔斯边界
- 批准号:
1607616 - 财政年份:2016
- 资助金额:
$ 15.76万 - 项目类别:
Continuing Grant
AWM-SIAM Workshop and Kovalevsky Lecture, 2014
AWM-SIAM 研讨会和 Kovalevsky 讲座,2014
- 批准号:
1346466 - 财政年份:2014
- 资助金额:
$ 15.76万 - 项目类别:
Standard Grant
AWM Workshops and Noether Lecture 2015, January 10-13, 2015; March 14-18, 2015
AWM 研讨会和 Noether 讲座 2015,2015 年 1 月 10-13 日;
- 批准号:
1440016 - 财政年份:2014
- 资助金额:
$ 15.76万 - 项目类别:
Standard Grant
Artin groups and CAT(0) spaces
Artin 群和 CAT(0) 空间
- 批准号:
1106726 - 财政年份:2011
- 资助金额:
$ 15.76万 - 项目类别:
Standard Grant
Mathematical Sciences: Research in Geometric Group Theory
数学科学:几何群论研究
- 批准号:
9208071 - 财政年份:1992
- 资助金额:
$ 15.76万 - 项目类别:
Continuing Grant
Mathematical Sciences: Research in Algebraic and Differential Topology
数学科学:代数和微分拓扑研究
- 批准号:
8607968 - 财政年份:1986
- 资助金额:
$ 15.76万 - 项目类别:
Continuing Grant
Mathematical Sciences: Research in Algebraic Topology, K-theory and Algebraic Geometry
数学科学:代数拓扑、K理论和代数几何研究
- 批准号:
8509397 - 财政年份:1985
- 资助金额:
$ 15.76万 - 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:
7919153 - 财政年份:1979
- 资助金额:
$ 15.76万 - 项目类别:
Fellowship Award
相似国自然基金
Lagrangian origin of geometric approaches to scattering amplitudes
- 批准号:24ZR1450600
- 批准年份:2024
- 资助金额:0.0 万元
- 项目类别:省市级项目
相似海外基金
Collaborative Research: Computational Geometric Uncertainty Propagation for Hamiltonian Systems on a Lie Group
合作研究:李群上哈密顿系统的计算几何不确定性传播
- 批准号:
1243000 - 财政年份:2012
- 资助金额:
$ 15.76万 - 项目类别:
Standard Grant
Collaborative Research: Computational Geometric Uncertainty Propagation for Hamiltonian Systems on a Lie Group
合作研究:李群上哈密顿系统的计算几何不确定性传播
- 批准号:
1029445 - 财政年份:2010
- 资助金额:
$ 15.76万 - 项目类别:
Standard Grant
Collaborative Research: Computational Geometric Uncertainty Propagation for Hamiltonian Systems on a Lie Group
合作研究:李群上哈密顿系统的计算几何不确定性传播
- 批准号:
1029551 - 财政年份:2010
- 资助金额:
$ 15.76万 - 项目类别:
Standard Grant
Collaborative Research: The Geometric Dual Space of A Unipotent Group in Characteristic p
合作研究:特征p中单能群的几何对偶空间
- 批准号:
1001660 - 财政年份:2010
- 资助金额:
$ 15.76万 - 项目类别:
Continuing Grant
Collaborative Research: The Geometric Dual Space of a Unipotent Group in Characteristic p
合作研究:特征p中单能群的几何对偶空间
- 批准号:
1001769 - 财政年份:2010
- 资助金额:
$ 15.76万 - 项目类别:
Continuing Grant
Research in geometric group theory
几何群论研究
- 批准号:
383958-2009 - 财政年份:2009
- 资助金额:
$ 15.76万 - 项目类别:
University Undergraduate Student Research Awards