FRG: Topological Invariants of 3 and 4-Manifolds
FRG:3 和 4 流形的拓扑不变量
基本信息
- 批准号:0244622
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2003
- 资助国家:美国
- 起止时间:2003-07-15 至 2008-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
DMS-0244622Selman AkbulutThis is a Division of Mathematical Sciences Focused Research Group (FRG) award made under solicitation http://www.nsf.gov/pubs/2002/nsf02129/nsf02129.htmThe goal of this proposal is to find purely topological (continuous orcombinatorial) definitions of the invariants arising out ofSeiberg-Witten theory. These include the basic classes for4-dimensional manifolds, and the Oszvath-Szabo Floer homology for3-manifolds. Recent progress, in particular the striking results ofOzsvath and Szabo in the last two years, has brought Seiberg-Wittentheory seemingly close to topology, and a concerted effort by thisgroup may be able finish the task.This proposal falls under the larger topics of gauge theory and stringtheory, which are closely connected to and motivated by theoreticalphysics, in particular the attempt to unify the forces of nature.Low-dimensional bordism theory is the mathematical analogue of n+1dimensional quantum field theories, i.e. an n-dimensional space and1-dimensional time correspond to an (n+1)-dimensional bordism betweentwo n-dimensional manifolds. These bordisms can have extra structure,e.g. contact structures in odd dimensions and symplectic structures ineven dimensions. Progress in understanding the mathematicalunderpinnings of this sort of physics feeds back into betterunderstanding of the physics.
DMS-0244622Selman AkbulutThis is a Division of Mathematical Sciences Focused Research Group (FRG) award made under solicitation http://www.nsf.gov/pubs/2002/nsf02129/nsf02129.htmThe goal of this proposal is to find purely topological (continuous orcombinatorial) definitions of the不变的理论出现了。 其中包括4维流形的基本类别,以及3-manifolds的Oszvath-Szabo浮动同源性。 最近的两年中,最近的进步,特别是在过去的两年中的惊人结果,使塞伯格·胜利(Seiberg-Wittentheory)看似接近拓扑结构,而本组的一致努力可能能够完成任务。这一建议属于较大的量学理论和弦乐的主题,这些理论与策略紧密相关,这些主题与特定的态度相关,尤其是企图,尤其是范围,尤其是在理论上的态度,尤其是在理论上的态度。理论是n+1维量子场理论的数学类似物,即n维空间和1维时间对应于n维歧管的(n+1) - 维界的bordism。 这些狂热可以具有额外的结构,例如。奇数维度和符号结构中的接触结构不超过11个维度。 理解这种物理学的数学指南的进展可以使物理学的更好地理解。
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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数据更新时间:2024-06-01
Selman Akbulut其他文献
Exotic rational surfaces without 1-handles
不带 1 控制柄的奇异有理曲面
- DOI:
- 发表时间:20072007
- 期刊:
- 影响因子:0
- 作者:Selman Akbulut;Kouichi Yasui;Kouichi Yasui;安井弘一;Kouichi YasuiSelman Akbulut;Kouichi Yasui;Kouichi Yasui;安井弘一;Kouichi Yasui
- 通讯作者:Kouichi YasuiKouichi Yasui
Computer graphics and minimal surfaces
计算机图形学和最小曲面
- DOI:
- 发表时间:20142014
- 期刊:
- 影响因子:0
- 作者:Selman Akbulut;安井弘一;Shoichi FujimoriSelman Akbulut;安井弘一;Shoichi Fujimori
- 通讯作者:Shoichi FujimoriShoichi Fujimori
Corks, Plugs and exotic structures
软木塞、塞子和奇异结构
- DOI:
- 发表时间:20082008
- 期刊:
- 影响因子:0
- 作者:Selman Akbulut;Kouichi YasuiSelman Akbulut;Kouichi Yasui
- 通讯作者:Kouichi YasuiKouichi Yasui
Exotic rational elliptic surfaces without 1-handles
不带 1 控制柄的奇异有理椭圆曲面
- DOI:
- 发表时间:
- 期刊:
- 影响因子:0
- 作者:Selman Akbulut;Kouichi Yasui;Kouichi YasuiSelman Akbulut;Kouichi Yasui;Kouichi Yasui
- 通讯作者:Kouichi YasuiKouichi Yasui
Contact 5-manifolds admitting open books with exotic Stein pages
接触 5-流形承认开放的书籍与异国情调的斯坦因页面
- DOI:
- 发表时间:20152015
- 期刊:
- 影响因子:0
- 作者:Selman Akbulut;安井弘一Selman Akbulut;安井弘一
- 通讯作者:安井弘一安井弘一
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Selman Akbulut的其他基金
Exotic 4- Manifolds, and geometric structures
奇异4-流形和几何结构
- 批准号:15053641505364
- 财政年份:2015
- 资助金额:----
- 项目类别:Standard GrantStandard Grant
Gokova Geometry/Topology Conference
Gokova几何/拓扑会议
- 批准号:15021351502135
- 财政年份:2015
- 资助金额:----
- 项目类别:Standard GrantStandard Grant
FRG: Collaborative Research: The topology and invariants of smooth 4-manifolds
FRG:协作研究:光滑4流形的拓扑和不变量
- 批准号:10658791065879
- 财政年份:2011
- 资助金额:----
- 项目类别:Continuing GrantContinuing Grant
Conference - Gokova Geometry/Topology Conference. To be held summer 2010-2014 in Turkey
会议 - Gokova 几何/拓扑会议。
- 批准号:10053661005366
- 财政年份:2010
- 资助金额:----
- 项目类别:Continuing GrantContinuing Grant
4-Manifolds, Calibrated Manifolds, Real Algebraic Varieties
4-流形、校准流形、实代数簇
- 批准号:09059170905917
- 财政年份:2009
- 资助金额:----
- 项目类别:Continuing GrantContinuing Grant
Gokova Geometry/Topology Conference
Gokova几何/拓扑会议
- 批准号:07071230707123
- 财政年份:2007
- 资助金额:----
- 项目类别:Standard GrantStandard Grant
4-Manifolds, Calibrated Manifolds, Real Algebraic Varieties
4-流形、校准流形、实代数簇
- 批准号:05056380505638
- 财政年份:2005
- 资助金额:----
- 项目类别:Standard GrantStandard Grant
Gokova Geometry/Topology Conference
Gokova几何/拓扑会议
- 批准号:04030960403096
- 财政年份:2004
- 资助金额:----
- 项目类别:Standard GrantStandard Grant
Topology of Smooth 4-Manifolds
光滑4流形拓扑
- 批准号:02045790204579
- 财政年份:2002
- 资助金额:----
- 项目类别:Continuing GrantContinuing Grant
Topology of Smooth 4-Manifolds
光滑4流形拓扑
- 批准号:99714409971440
- 财政年份:1999
- 资助金额:----
- 项目类别:Standard GrantStandard Grant
相似国自然基金
扭曲边界条件下的拓扑不变量及其实空间表示
- 批准号:12247134
- 批准年份:2022
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高rho不变量在几何拓扑中的应用
- 批准号:11901374
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超导线路中的拓扑量子模拟与测量
- 批准号:11904111
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拟拓扑群中若干问题的研究
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拓扑不变量: 空间的结构及其自映射
- 批准号:11961131004
- 批准年份:2019
- 资助金额:120 万元
- 项目类别:国际(地区)合作与交流项目
相似海外基金
Constraints and topological invariants
约束和拓扑不变量
- 批准号:572440-2022572440-2022
- 财政年份:2022
- 资助金额:----
- 项目类别:University Undergraduate Student Research AwardsUniversity Undergraduate Student Research Awards
Knot invariants and topological recursion
结不变量和拓扑递归
- 批准号:573166-2022573166-2022
- 财政年份:2022
- 资助金额:----
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Construction and Classification of Weaves
组织结构和分类
- 批准号:22J1339722J13397
- 财政年份:2022
- 资助金额:----
- 项目类别:Grant-in-Aid for JSPS FellowsGrant-in-Aid for JSPS Fellows
Knotted surface invariants from 4-dimensional topological quantum field theories
4 维拓扑量子场论的打结表面不变量
- 批准号:532076-2019532076-2019
- 财政年份:2021
- 资助金额:----
- 项目类别:Postdoctoral FellowshipsPostdoctoral Fellowships
A new look into various arithmetic and topological invariants through the eyes of modular knots
从模结的角度重新审视各种算术和拓扑不变量
- 批准号:21K1814121K18141
- 财政年份:2021
- 资助金额:----
- 项目类别:Grant-in-Aid for Challenging Research (Pioneering)Grant-in-Aid for Challenging Research (Pioneering)