Group Actions on Hyperbolic Spaces

双曲空间上的群作用

基本信息

  • 批准号:
    2106906
  • 负责人:
  • 金额:
    $ 26.4万
  • 依托单位:
  • 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 2025-06-30
  • 项目状态:
    未结题

项目摘要

The collection of symmetries of an object form an algebraic object called a group. A simple example of a group is that of reflections and rotations of a square, as in the case of a 90 degree rotation, which leaves it unchanged. Studying groups can lead to many interesting questions. One could ask, for instance, how many different groups act on a square? What do such groups have in common? Geometric group theory aims to answer such questions by translating the geometric properties of spaces on which a group acts into algebraic properties of the group. The project will use these techniques to work towards understanding certain classes of groups, all of which act on spaces that have a particular geometric structure, called hyperbolicity. This project also seeks to support and encourage student involvement in mathematics, through support for graduate students, outreach to the local community, and support for a seminar series.In more detail, this projects fits into the broad goal of understanding groups that act on hyperbolic, or negatively curved, spaces. This goal is approached in three distinct ways: first, through understanding all actions of a given group on hyperbolic metric spaces; next, through an in-depth study of two particular actions of big mapping class groups, a class of groups in which there has recently been an explosion of interest; and finally, by seeking to prove a strong stability result for quotients of hierarchically hyperbolic groups, a class of groups which can be completely described by their actions on hyperbolic metric spaces. Parts of this project involve tools from other areas of mathematics, including descriptive set theory and (often non-commutative) ring theory.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.
一个对象的对称性的集合形成一个代数对象,称为群。 一个简单的例子是一个正方形的反射和旋转,就像90度旋转一样,它保持不变。 研究小组可以引出许多有趣的问题。例如,人们可以问,有多少不同的群体在一个正方形上活动? 这些群体有什么共同点? 几何群论旨在通过将群作用于其上的空间的几何性质转化为群的代数性质来回答这些问题。该项目将使用这些技术来理解某些类别的群体,所有这些群体都作用于具有特定几何结构的空间,称为双曲面。 该项目还寻求支持和鼓励学生参与数学,通过支持研究生,推广到当地社区,并支持一系列研讨会。更详细地说,该项目符合理解双曲或负弯曲空间上的群体的广泛目标。 这个目标是接近在三个不同的方式:首先,通过了解所有的行动,一个给定的组双曲度量空间;其次,通过深入研究两个特定的行动大映射类组,一类的群体,其中最近有一个爆炸的兴趣;最后,通过试图证明一个强稳定性的结果,一类可以完全由它们在双曲度量空间上的作用来描述的群。 该项目的部分内容涉及数学其他领域的工具,包括描述性集合论和(通常是非交换的)环理论。该奖项反映了NSF的法定使命,并通过使用基金会的知识价值和更广泛的影响审查标准进行评估,被认为值得支持。

项目成果

期刊论文数量(2)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Higher rank confining subsets and hyperbolic actions of solvable groups
可解群的高阶限制子集和双曲行为
  • DOI:
    10.1016/j.aim.2023.109045
  • 发表时间:
    2023
  • 期刊:
  • 影响因子:
    1.7
  • 作者:
    Abbott, Carolyn R.;H Balasubramanya, Sahana;Rasmussen, Alexander J.
  • 通讯作者:
    Rasmussen, Alexander J.
Largest hyperbolic actions and quasi-parabolic actions in groups
群中最大双曲作用和拟抛物线作用
  • DOI:
    10.1142/s1793525322500066
  • 发表时间:
    2022
  • 期刊:
  • 影响因子:
    0.8
  • 作者:
    Abbott, Carolyn R.;Rasmussen, Alexander J.
  • 通讯作者:
    Rasmussen, Alexander J.
{{ 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 }}

Carolyn Abbott其他文献

Carolyn Abbott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('Carolyn Abbott', 18)}}的其他基金

CAREER: Large scale geometry and negative curvature
职业:大规模几何和负曲率
  • 批准号:
    2340341
  • 财政年份:
    2024
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Continuing Grant
PostDoctoral Research Fellowship
博士后研究奖学金
  • 批准号:
    1803368
  • 财政年份:
    2018
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Fellowship Award

相似海外基金

Currents on hyperbolic surfaces and non-cocompact group actions
双曲曲面上的流和非余紧群作用
  • 批准号:
    22KJ2645
  • 财政年份:
    2023
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Grant-in-Aid for JSPS Fellows
Smooth 4-Manifold Topology, 3-Manifold Group Actions, the Heegaard Tree, and Low Volume Hyperbolic 3-Manifolds
平滑 4 流形拓扑、3 流形组动作、Heegaard 树和低容量双曲 3 流形
  • 批准号:
    2003892
  • 财政年份:
    2020
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Continuing Grant
Actions of Relatively Hyperbolic Groups on Cube Complexes
立方复形上相对双曲群的作用
  • 批准号:
    1904913
  • 财政年份:
    2019
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Continuing Grant
Geometry of hyperbolic groups and of their actions on Banach spaces
双曲群的几何及其在巴纳赫空间上的作用
  • 批准号:
    2099922
  • 财政年份:
    2018
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Studentship
Relatively hyperbolic structures and convergence actions of discrete groups
离散群的相对双曲结构和收敛作用
  • 批准号:
    24740045
  • 财政年份:
    2012
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Grant-in-Aid for Young Scientists (B)
RUI: Cocycles and rigidity for hyperbolic systems and actions
RUI:双曲系统和作用的余循环和刚度
  • 批准号:
    1101150
  • 财政年份:
    2011
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Standard Grant
Actions of Groups on Hyperbolic Spaces
双曲空间上的群的作用
  • 批准号:
    0804369
  • 财政年份:
    2008
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Standard Grant
Rigidity of partially hyperbolic dynamical systems and actions of solvable Lie groups
部分双曲动力系统的刚性和可解李群的作用
  • 批准号:
    19740085
  • 财政年份:
    2007
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Grant-in-Aid for Young Scientists (B)
Cohomology of Dynamical Systems, Rigidity of Smooth Group Actions, and Partially Hyperbolic Diffeomorphisms
动力系统的上同调、光滑群作用的刚性和部分双曲微分同胚
  • 批准号:
    0196530
  • 财政年份:
    2001
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Standard Grant
Cohomology of Dynamical Systems, Rigidity of Smooth Group Actions, and Partially Hyperbolic Diffeomorphisms
动力系统的上同调、光滑群作用的刚性和部分双曲微分同胚
  • 批准号:
    9971826
  • 财政年份:
    1999
  • 资助金额:
    $ 26.4万
  • 项目类别:
    Standard Grant
{{ showInfoDetail.title }}

作者:{{ showInfoDetail.author }}

知道了