String Topology and the Algebraic Topology of Moduli Spaces
弦拓扑和模空间的代数拓扑
基本信息
- 批准号:0603713
- 负责人:
- 金额:$ 42.05万
- 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 2010-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This proposal consists of several projects using algebraic topological techniques to study geometric questions arising in String Topology, and the topology of moduli spaces. The theory of String Topology, first introduced by Chas and Sullivan in 1999, now involves a vast array of rich structure on spaces of paths and loops of manifolds, as well as maps from surfaces to manifolds. In this proposal, Cohen will emphasize applications of string topology, and the recent breakthroughs in the study of the homotopy type of moduli spaces. These applications will be both to geometry (understanding the Gromov-Witten theory of cotangent bundles, and the cobordism type of moduli spaces of holomorphic curves), and within algebraic topology (the K -theory of loop spaces of classifying spaces, twisted equivariant K -theory, and Waldhausen's algebraic K -theory of spaces). Cohen, in collaboration with I. Madsen, will also study the homotopy type of moduli spaces of maps of surfaces, extending Madsen and Weiss's recent work on the generalized Mumford conjecture. They propose a longer term project to use this knowledge, as well as an adaptation of string topology methods, to understand bordism classes represented by the compact moduli spaces of stable holomorphic curves in a symplectic manifold. This proposal consists of several projects investigating the new area of research known as "String Topology", as well as related questions. String topology, a theory that was first introduced by Chas and Sullivan in 1999, studies structures on spaces of paths, loops, and surfaces. This structure was motivated by formalisms in string theory in physics. The idea is to understand how loops (or paths) in a background space can evolve in time. Loops can evolve by changing in size and even breaking apart. These phenomena are measured by studying surfaces mapping to the background space, that span these loops. In this project, Cohen tends to study the intersection properties of these spaces of loops and surfaces, and in particular the topology of the space of surfaces mapping to a background space. His goal is to apply these constructions to a variety of geometric questions.
该提案由几个使用代数拓扑技术来研究弦拓扑和模空间拓扑中出现的几何问题的项目组成。 弦拓扑理论由 Chas 和 Sullivan 于 1999 年首次提出,现在涉及流形路径和循环空间上的大量丰富结构,以及从曲面到流形的映射。 在这个提案中,科恩将强调弦拓扑的应用,以及模空间同伦型研究的最新突破。这些应用既适用于几何学(理解余切丛的格罗莫夫-维滕理论和全纯曲线模空间的配边类型),也适用于代数拓扑(分类空间的循环空间的 K 理论、扭曲等变 K 理论和 Waldhausen 的代数 K 空间理论)。 科恩与 I. Madsen 合作,还将研究曲面图模空间的同伦类型,扩展 Madsen 和 Weiss 最近关于广义芒福德猜想的工作。 他们提出了一个长期项目,利用这些知识以及弦拓扑方法的改进,来理解由辛流形中稳定全纯曲线的紧模空间表示的棱主义类。 该提案由几个项目组成,调查被称为“弦拓扑”的新研究领域以及相关问题。 弦拓扑是 Chas 和 Sullivan 于 1999 年首次提出的理论,研究路径、环路和曲面空间的结构。 这种结构是受到物理学弦理论形式主义的启发。 这个想法是为了理解背景空间中的循环(或路径)如何随时间演变。循环可以通过改变大小甚至分裂来演变。 这些现象是通过研究映射到跨越这些环的背景空间的表面来测量的。 在这个项目中,科恩倾向于研究这些环和曲面空间的相交属性,特别是映射到背景空间的曲面空间的拓扑。 他的目标是将这些构造应用于各种几何问题。
项目成果
期刊论文数量(0)
专著数量(0)
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会议论文数量(0)
专利数量(0)
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Ralph Cohen其他文献
Factors affecting 13C-natural abundance measurement of breath carbon dioxide during surgery: absorption of carbon dioxide during endoscopic procedures.
影响手术期间呼吸二氧化碳 13C 自然丰度测量的因素:内窥镜手术期间二氧化碳的吸收。
- DOI:
10.1002/rcm.3572 - 发表时间:
2008 - 期刊:
- 影响因子:0
- 作者:
S. Eaton;M. Pacilli;James Wood;M. McHoney;L. Corizia;C. Kingsley;J. Curry;J. Herod;Ralph Cohen;A. Pierro - 通讯作者:
A. Pierro
Vanishing lines in generalized Adams spectral sequences are generic
广义 Adams 谱序列中的消失线是通用的
- DOI:
10.2140/gt.1999.3.155 - 发表时间:
1999 - 期刊:
- 影响因子:2
- 作者:
Geometry Topology;G. G G G G G G G G G G G G G G;M. Hopkins;J. Palmieri;J. Smith;Ralph Cohen;Gunnar Carlsson - 通讯作者:
Gunnar Carlsson
Innovation and variation: Literary change and georgic poetry
- DOI:
10.1007/bf02029080 - 发表时间:
1975-03-01 - 期刊:
- 影响因子:0.200
- 作者:
Ralph Cohen - 通讯作者:
Ralph Cohen
Role of simulation for paediatric proceduralists: Practice makes perfect or trial and error?
模拟对儿科程序学家的作用:熟能生巧还是反复试验?
- DOI:
10.1111/jpc.12039 - 发表时间:
2013 - 期刊:
- 影响因子:1.7
- 作者:
S. S. Bidarkar;James Wood;Ralph Cohen;A. Holland - 通讯作者:
A. Holland
Transitional cell papilloma of the bladder in a child: A case report and review of literature
- DOI:
10.1016/j.jpurol.2005.05.009 - 发表时间:
2006-02-01 - 期刊:
- 影响因子:
- 作者:
Gordon Thomas;Parshotam Gera;Susan Arbuckle;Ralph Cohen - 通讯作者:
Ralph Cohen
Ralph Cohen的其他文献
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{{ truncateString('Ralph Cohen', 18)}}的其他基金
String Topology, Field Theories, and the Topology of Moduli Spaces
弦拓扑、场论和模空间拓扑
- 批准号:
1104555 - 财政年份:2011
- 资助金额:
$ 42.05万 - 项目类别:
Continuing Grant
String Topology, Field Theories, and the Topology of Moduli Spaces
弦拓扑、场论和模空间拓扑
- 批准号:
0905809 - 财政年份:2009
- 资助金额:
$ 42.05万 - 项目类别:
Standard Grant
An International Conference on: New Challenges and Perspectives in Symplectic Field Theory
国际会议:辛场论的新挑战和前景
- 批准号:
0649446 - 财政年份:2007
- 资助金额:
$ 42.05万 - 项目类别:
Standard Grant
SM: Geometry and Topology of Moduli Spaces and Applications
SM:模空间的几何和拓扑及其应用
- 批准号:
0603355 - 财政年份:2006
- 资助金额:
$ 42.05万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Moduli Spaces of Riemann Surfaces and String Topology
FRG:协作研究:黎曼曲面和弦拓扑的模空间
- 批准号:
0244550 - 财政年份:2003
- 资助金额:
$ 42.05万 - 项目类别:
Standard Grant
Workshop on the Mumford Standard Class Conjecture at Stanford University, July and August, 2001.
芒福德标准类猜想研讨会,斯坦福大学,2001 年 7 月和 8 月。
- 批准号:
0115014 - 财政年份:2001
- 资助金额:
$ 42.05万 - 项目类别:
Standard Grant
Presidential Young Investigator: Mathematical Sciences: Algebraic and Differential Topology
总统青年研究员:数学科学:代数和微分拓扑
- 批准号:
8352122 - 财政年份:1984
- 资助金额:
$ 42.05万 - 项目类别:
Continuing Grant
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