Topology of low dimensional manifolds with various geometric structures

具有各种几何结构的低维流形拓扑

• 批准号: 20540072
• 负责人: UE Masaaki
• 金额: $ 2.25万
• 依托单位: Kyoto University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540072/
• 关键词: 微分トポロジー; 3次元多様体; 4次元多様体; Seiberg-Witten理論; 不変量; ホモロジー3球面; フレアホモロジー; 球面多様体; 鉛管多様体; 幾何学; トポロジー; Floerホモロジー; Seiber-Witten理論; 有理ホモロジー3球面

Masaaki Ue, the representative of this research has studied 3 and 4-manifolds, in particular 4-manifolds with boundary. We show that the two invariants for 3-manifolds, which are called Fukumoto-Furuta invariant and the correction term, coincide in case of spherical 3-manifolds. These invariants are derived from the two important theories for this area of research, Seiberg-Witten theory and Heegaard Floer homology theory. Moreover we show that these invariants are represented by the previously known eta invariants. We also give explicit constraints for the structures of 4-manifolds bounded by 3-manifolds of this type in terms of the Fukumoto-Furuta invariant.

本研究的代表人物Masaaki Ue研究了3流形和4流形，特别是带边界的4流形。我们证明了3-流形的两个不变量（称为Fukumoto-Furuta不变量和校正项）在球面3-流形中重合。这些不变量来源于这一研究领域的两个重要理论，Seiberg-Witten理论和Heegaard Floer同调理论。此外，我们证明了这些不变量由先前已知的不变量表示。我们还利用Fukumoto-Furuta不变量给出了由这类3-流形约束的4-流形结构的显式约束。

项目成果

Geometric representations of interacting maps

交互地图的几何表示

• 发表时间: 2010
• 期刊: International Journal of Mathematics and Mathematical Sciences
• 影响因子: 1.2
• 作者: Y. Hemmi;T. Kobayashi;Min Lwin Oo;廣瀬進;廣瀬進;廣瀬進;廣瀬進;廣瀬進;廣瀬進;廣瀬進;Tsuyoshi Kato
• 通讯作者: Tsuyoshi Kato

Growth of Casson handles and smooth structure o n 4-manifolds

Casson 手柄的生长和 4 歧管上的平滑结构

• 发表时间: 2010
• 作者: J.Itoh;C.Vilcu;加藤毅
• 通讯作者: 加藤毅

A rough equivalence on partial differential equations, Geometry and Analysis

偏微分方程、几何与分析的粗略等价

• 发表时间: 2009
• 作者: J. Itoh;L-Yuan;加藤毅
• 通讯作者: 加藤毅

An index theory over Casson handles and complexity of smooth structure on K3 surface

卡森柄指数理论与K3表面光滑结构复杂度

• 发表时间: 2009
• 作者: H.Endo;D.Kotschick;M. Morimoto;加藤毅;遠藤 入顕;T. Kato;M. Morimoto;遠藤久顕;M. Morimoto;Tsuyoshi Kato
• 通讯作者: Tsuyoshi Kato

Growth of Casson handles and smooth structures on 4-manifolds

Casson 手柄和 4 歧管上光滑结构的生长

• 发表时间: 2010
• 作者: J.Itoh;C.Vilcu;廣瀬進;Tsuyoshi Kato
• 通讯作者: Tsuyoshi Kato