4-Manifolds, Calibrated Manifolds, Real Algebraic Varieties
4-流形、校准流形、实代数簇
基本信息
- 批准号:0505638
- 负责人:
- 金额:$ 10.8万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2005
- 资助国家:美国
- 起止时间:2005-07-15 至 2008-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Proposer plans to investigate the topology of smooth 4-manifolds by attacking some unsolved problems in 4-manifolds by decomposing them into basic easy to understand pieces (PALF's), and studying the pieces by applying techniques of complex and symplectic manifold theory. He also plans to work on calibrated manifolds, and on real algebraic varieties. In particular he plans to study on certain classes of 7 and 8 dimensional manifolds (so called G2 and Spin(7) manifolds); by studying the certain families of 3 and 4 dimensional submanifolds in them (so called associative and Cayley submanifolds) Proposer hopes to get a global understanding of the gauge theories of low dimensional manifolds, and construct a counting theory for these submanifolds (similar to Gromov-Witten counting theory of holomorphic curves in symplectic manifolds). Also, Proposer wants to continue to work on the project of topological characterization of real algebraic sets.Three and four dimensional manifolds, and certain classes of seven and eight dimensional manifolds (so called G2 and Spin(7) manifolds) are current interest of physicist because they play central role in understanding of space-time and the String theory physics. Also, algebraic sets are a nice way to describe topological spaces in equations, but not all the topological spaces can be described this way. Proposal plans to characterize all the topological spaces that can be described as real algebraic sets.
Proposer计划研究光滑4-流形的拓扑结构,通过将4-流形中的一些未解决的问题分解为基本的易于理解的片段(PALF),并通过应用复流形和辛流形理论的技术来研究这些片段。他还计划工作的校准流形,并对真实的代数品种。特别是他计划研究某些类的7和8维流形(所谓的G2和Spin(7)流形);通过研究其中的某些三维和四维子流形族,(所谓的结合和凯莱子流形)提案者希望得到一个全球性的理解规范理论的低维流形,并为这些子流形构造一个计数理论(类似于辛流形中全纯曲线的Gromov-Witten计数理论)。此外,Proposer希望继续致力于真实的代数集的拓扑特征的项目。三维和四维流形,以及某些类的七维和八维流形(所谓的G2和Spin(7)流形)是物理学家目前的兴趣,因为它们在理解时空和弦论物理中起着核心作用。此外,代数集是用方程描述拓扑空间的一种很好的方法,但不是所有的拓扑空间都可以用这种方法描述。建议计划的特点是所有的拓扑空间,可以描述为真实的代数集。
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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Selman Akbulut其他文献
A topological resolution theorem
- DOI:
10.1007/bf02698689 - 发表时间:
1981-12-01 - 期刊:
- 影响因子:3.500
- 作者:
Selman Akbulut;Laurence Taylor - 通讯作者:
Laurence Taylor
Exotic rational surfaces without 1-handles
不带 1 控制柄的奇异有理曲面
- DOI:
- 发表时间:
2007 - 期刊:
- 影响因子:0
- 作者:
Selman Akbulut;Kouichi Yasui;Kouichi Yasui;安井弘一;Kouichi Yasui - 通讯作者:
Kouichi Yasui
Computer graphics and minimal surfaces
计算机图形学和最小曲面
- DOI:
- 发表时间:
2014 - 期刊:
- 影响因子:0
- 作者:
Selman Akbulut;安井弘一;Shoichi Fujimori - 通讯作者:
Shoichi Fujimori
Real algebraic structures on topological spaces
- DOI:
10.1007/bf02698688 - 发表时间:
1981-12-01 - 期刊:
- 影响因子:3.500
- 作者:
Selman Akbulut;Henry C. King - 通讯作者:
Henry C. King
Corks and exotic ribbons in $$B^{4}$$
- DOI:
10.1007/s40879-022-00581-1 - 发表时间:
2022-09-19 - 期刊:
- 影响因子:0.500
- 作者:
Selman Akbulut - 通讯作者:
Selman Akbulut
Selman Akbulut的其他文献
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{{ truncateString('Selman Akbulut', 18)}}的其他基金
Exotic 4- Manifolds, and geometric structures
奇异4-流形和几何结构
- 批准号:
1505364 - 财政年份:2015
- 资助金额:
$ 10.8万 - 项目类别:
Standard Grant
Gokova Geometry/Topology Conference
Gokova几何/拓扑会议
- 批准号:
1502135 - 财政年份:2015
- 资助金额:
$ 10.8万 - 项目类别:
Standard 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:
1065879 - 财政年份:2011
- 资助金额:
$ 10.8万 - 项目类别:
Continuing 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:
1005366 - 财政年份:2010
- 资助金额:
$ 10.8万 - 项目类别:
Continuing Grant
4-Manifolds, Calibrated Manifolds, Real Algebraic Varieties
4-流形、校准流形、实代数簇
- 批准号:
0905917 - 财政年份:2009
- 资助金额:
$ 10.8万 - 项目类别:
Continuing Grant
Gokova Geometry/Topology Conference
Gokova几何/拓扑会议
- 批准号:
0707123 - 财政年份:2007
- 资助金额:
$ 10.8万 - 项目类别:
Standard Grant
Gokova Geometry/Topology Conference
Gokova几何/拓扑会议
- 批准号:
0403096 - 财政年份:2004
- 资助金额:
$ 10.8万 - 项目类别:
Standard Grant
FRG: Topological Invariants of 3 and 4-Manifolds
FRG:3 和 4 流形的拓扑不变量
- 批准号:
0244622 - 财政年份:2003
- 资助金额:
$ 10.8万 - 项目类别:
Standard Grant
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