Topology related to Mathematical Physics, Morse Theory and Numerical Computations
与数学物理、莫尔斯理论和数值计算相关的拓扑
基本信息
- 批准号:16540056
- 负责人:
- 金额:$ 2.18万
- 依托单位:
- 依托单位国家:日本
- 项目类别:Grant-in-Aid for Scientific Research (C)
- 财政年份:2004
- 资助国家:日本
- 起止时间:2004 至 2006
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Previously, Professors M.Guest, A.Kozlowski and the author showed that the Atiyah-Jones-Segal type Theorem holds for spaces of holomorphic maps from the 1 dimensional complex projective space to certain family of complex projective varieties. Now he showed that a similar result holds for certain subspaces of them which are defined by using the concept of multiplicities induced from the representations of polynomials of holomorphic maps. Furthermore, he computed the fundamental groups for spaces of self-holomorphic maps on the n dimensional complex Projective spaces.Until now, we usually investigate whether AJS type Theorem holds or not for spaces of holomorphic (or algebraic) maps from one real dimensional (or complex one dimensional) spaces. In our investigation, now we can investigate whether such a problem for spaces of holomorphic or algebraic maps from high dimensional spaces. As one example, we can show that the spaces of regular maps from certain compact affine spaces into complex or real Grassmanian manifolds are homotopy equivalent of spaces of continuous maps between these spaces if these varieties Affine spaces satisfy certain conditions of vector bundles, which is one of joint works with Professor A. Kozlowski. To prove these results, we use the technique of real algebraic geometry. Moreover, we can prove that AJS type Theorem holds for such spaces by using the above Theorem. In particular, we also determine the fundamental groups of spaces of maps from m dimensional real projective space into n dimensional one when m=n-1, or m=n. Such a result can be regarded as a real version of the study investigated in the above first case.We also study the exceptional surgery from the new point view of singularity theory by using the divide theory. In particular, we study the mechanism of such surgeries and the structure of the set of exceptional surgeries.
在此之前,M.Guest,A.Kozlowski教授和作者证明了Atiyah-Jones-Segal型定理对于从1维复射影空间到某一族复射影体族的全纯映射空间成立。现在,他证明了类似的结果也适用于它们的某些子空间,这些子空间是由全纯映射的多项式的表示导出的重数的概念定义的。此外,他还计算了n维复射影空间上自全纯映射空间的基本群。直到现在,我们通常都在研究AJS型定理对于一维(或一维复数)空间的全纯(或代数)映射空间是否成立。在我们的研究中,我们现在可以研究高维空间中的全纯映射或代数映射空间是否存在这样的问题。作为一个例子,我们可以证明从某些紧仿射空间到复或实Grassmanian流形的正则映射空间是这些空间之间的连续映射空间的同伦等价,如果这些簇仿射空间满足向量丛的某些条件,这是A.Kozlowski教授的共同工作之一。为了证明这些结果,我们使用了实代数几何的技巧。此外,我们还利用上述定理证明了AJS型定理在此类空间中成立。特别地,当m=n-1或m=n时,我们还确定了从m维实射影空间到n维实射影空间的映射的基本群.这样的结果可以看作上述第一种情况下研究的实数版.我们还利用除法理论从奇点理论的新角度研究了例外运算.特别是,我们研究了这类手术的机制和例外手术集的结构。
项目成果
期刊论文数量(74)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
The homotopy of spaces of maps between real projective spaces
实射影空间之间的映射空间的同伦
- DOI:
- 发表时间:2006
- 期刊:
- 影响因子:0
- 作者:小島定吉;糸川銚;酒井隆;戸田正人;小林治;二木昭人;浦川肇;十文字正樹;山口孝男;塩谷隆;小林亮一;T.Sakai;T. Sakai;Shingo Okuyama;Kazuhisa Shimakawa;Kohhei Yamaguchi
- 通讯作者:Kohhei Yamaguchi
New characterizations of exponential dichotomy and exponential stability of linear differential equations
线性微分方程指数二分法和指数稳定性的新表征
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:P.H.A.Ngoc;T.Naito
- 通讯作者:T.Naito
Homotopy types of m-twisted CP^4's
m-扭曲 CP^4 的同伦类型
- DOI:
- 发表时间:2005
- 期刊:
- 影响因子:0
- 作者:Juno Mukai;Kohhei Yamaguchi;Kohhei Yamaguchi;Kohhei Yamaguchi
- 通讯作者:Kohhei Yamaguchi
$D$-stability radius of linear discrete time ststems
$D$-线性离散时间稳定性半径
- DOI:
- 发表时间:2006
- 期刊:
- 影响因子:0
- 作者:N.Pham Huu Anh;T.Naito
- 通讯作者:T.Naito
{{
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 }}
YAMAGUCHI Kohhei其他文献
YAMAGUCHI Kohhei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('YAMAGUCHI Kohhei', 18)}}的其他基金
Homotopy types of spaces of rational curves on a toric manifold and related geometry
复曲面流形上有理曲线空间的同伦类型及相关几何
- 批准号:
18K03295 - 财政年份:2018
- 资助金额:
$ 2.18万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
Applications of real singularity theory and the homotopy types of spaces of holomorphic maps
实奇点理论与全纯映射空间同伦型的应用
- 批准号:
26400083 - 财政年份:2014
- 资助金额:
$ 2.18万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
The spaces of regular maps and the applications of real singularity theory to homotopy theory
正则映射空间及实奇点理论在同伦理论中的应用
- 批准号:
23540079 - 财政年份:2011
- 资助金额:
$ 2.18万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
RESEARCH OF TOPOLOGY RELATED THE MORSE THEORY AND RESEARCH OF COMPUTER ALGRBRA SYSTEM
莫尔斯理论相关拓扑研究与计算机代数系统研究
- 批准号:
19540068 - 财政年份:2007
- 资助金额:
$ 2.18万 - 项目类别:
Grant-in-Aid for Scientific Research (C)
相似海外基金
Polynomial Interpolation, Symmetric Ideals, and Lefschetz Properties
多项式插值、对称理想和 Lefschetz 属性
- 批准号:
2401482 - 财政年份:2024
- 资助金额:
$ 2.18万 - 项目类别:
Continuing Grant
New Frontiers in Large-Scale Polynomial Optimisation
大规模多项式优化的新领域
- 批准号:
DE240100674 - 财政年份:2024
- 资助金额:
$ 2.18万 - 项目类别:
Discovery Early Career Researcher Award
Collaborative Research: AF: Small: Real Solutions of Polynomial Systems
合作研究:AF:小:多项式系统的实数解
- 批准号:
2331401 - 财政年份:2024
- 资助金额:
$ 2.18万 - 项目类别:
Standard Grant
Collaborative Research: AF: Small: Real Solutions of Polynomial Systems
合作研究:AF:小:多项式系统的实数解
- 批准号:
2331400 - 财政年份:2024
- 资助金额:
$ 2.18万 - 项目类别:
Standard Grant
Parent-adolescent informant discrepancies: Predicting suicide risk and treatment outcomes
父母与青少年信息差异:预测自杀风险和治疗结果
- 批准号:
10751263 - 财政年份:2024
- 资助金额:
$ 2.18万 - 项目类别:
CAREER: Low-Degree Polynomial Perspectives on Complexity
职业:复杂性的低次多项式视角
- 批准号:
2338091 - 财政年份:2024
- 资助金额:
$ 2.18万 - 项目类别:
Continuing Grant
Supersymmetry in the geometry of particle systems
粒子系统几何中的超对称性
- 批准号:
23K12983 - 财政年份:2023
- 资助金额:
$ 2.18万 - 项目类别:
Grant-in-Aid for Early-Career Scientists
DDALAB: Identifying Latent States from Neural Recordings with Nonlinear Causal Analysis
DDALAB:通过非线性因果分析从神经记录中识别潜在状态
- 批准号:
10643212 - 财政年份:2023
- 资助金额:
$ 2.18万 - 项目类别:
A Gene-Network Discovery Approach to Structural Brain Disorders
结构性脑疾病的基因网络发现方法
- 批准号:
10734863 - 财政年份:2023
- 资助金额:
$ 2.18万 - 项目类别:
A novel instrument for continuous blood pressure monitoring
一种新型连续血压监测仪器
- 批准号:
10696510 - 财政年份:2023
- 资助金额:
$ 2.18万 - 项目类别: