"Manifolds, knots and groups"
“流形、结和组”
基本信息
- 批准号:8082-2012
- 负责人:
- 金额:$ 1.53万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2015
- 资助国家:加拿大
- 起止时间:2015-01-01 至 2016-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Three-dimensional manifolds describe the possible shapes of our universe, and also arise in many applications such as dynamical systems. The proposal is to develop algebraic and geometric tools to apply toward our deeper understanding of 3-manifolds and their structure. These tools are also useful in the theory of knots and other topological phenomena.
Specifically, a manifold or a knot has an algebraic system, called a "group", associated with it. A celebrated conjecture of Poincare, which was solved recently by Perelman, is that if the group reduces to a single element, then the manifold is determined to be simply a 3-dimensional sphere. More generally this group gives computable information about the overall shape of the manifold or knot. By considering appropriate orderings of the objects in the group, we can sharpen the information available. Such ordered groups, in recent years, have uncovered new properties of knots and 3-dimensional manifolds not available before. This is an ongoing, exciting new development in the application of algebra to geometric topology, with much yet to be discovered.
三维流形描述了我们宇宙的可能形状,也出现在许多应用中,如动力系统。 该计划旨在开发代数和几何工具,以帮助我们更深入地理解三维流形及其结构。 这些工具在纽结和其他拓扑现象的理论中也很有用。
具体地说,流形或纽结有一个代数系统,称为“群”,与之相关联。庞加莱的一个著名猜想,最近由佩雷尔曼解决,是如果群简化为一个单一的元素,那么流形被确定为简单的三维球体。 更一般地说,这一组给出了关于流形或纽结的整体形状的可计算信息。 通过考虑组中对象的适当排序,我们可以使可用的信息更加清晰。 近年来,这种有序群揭示了以前没有的纽结和三维流形的新性质。 这是一个正在进行的,令人兴奋的新发展,在应用代数几何拓扑,还有很多有待发现。
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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Rolfsen, Dale其他文献
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{{ truncateString('Rolfsen, Dale', 18)}}的其他基金
Manifolds and Groups
流形和组
- 批准号:
RGPIN-2017-03750 - 财政年份:2021
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
Manifolds and Groups
流形和组
- 批准号:
RGPIN-2017-03750 - 财政年份:2020
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
Manifolds and Groups
流形和组
- 批准号:
RGPIN-2017-03750 - 财政年份:2019
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
Manifolds and Groups
流形和组
- 批准号:
RGPIN-2017-03750 - 财政年份:2018
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
Manifolds and Groups
流形和组
- 批准号:
RGPIN-2017-03750 - 财政年份:2017
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
"Manifolds, knots and groups"
“流形、结和组”
- 批准号:
8082-2012 - 财政年份:2014
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
"Manifolds, knots and groups"
“流形、结和组”
- 批准号:
8082-2012 - 财政年份:2013
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
"Manifolds, knots and groups"
“流形、结和组”
- 批准号:
8082-2012 - 财政年份:2012
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
Algebraic and geometric topology
代数和几何拓扑
- 批准号:
8082-2007 - 财政年份:2011
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
Algebraic and geometric topology
代数和几何拓扑
- 批准号:
8082-2007 - 财政年份:2010
- 资助金额:
$ 1.53万 - 项目类别:
Discovery Grants Program - Individual
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