课题基金 / 基金详情

Geometry of Groups and Moduli Spaces (2)

Geometry of Groups and Moduli Spaces (2)
群和模空间的几何(2)
批准号:
19204003
负责人:
MORITA Shigeyuki
金额:
$12.73万
依托单位:
依托单位国家:
日本
项目类别:
Grant-in-Aid for Scientific Research (A)
财政年份:
2007
资助国家:
日本
项目状态:
已结题
起止时间:
2007 至 2009

项目摘要

项目成果

MORITA Shigeyuki的其他基金

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相关文献

中文摘要
翻译
黎曼曲面的模空间和图的模空间及其相关的模群,如曲面的映射类群和自由群的自同构群,是代数几何、复分析、微分几何、拓扑学和数学物理等多个数学分支的重要研究课题。本文主要从拓扑学的角度对这些模空间和模群进行了研究,得到了许多有趣的结果。此外,我们还得到了与三维流形、四维流形和横辛叶理论密切相关的新结果和猜想。我们还向包括数论在内的新的研究方向提出了一个深层次的问题。
英文摘要
The moduli space of Riemann surfaces and the moduli space of graphs, as well as their associated modular groups such as the mapping class groups of surfaces and the automorphism groups of free groups, are among the most important research subjects of diverse branches of mathematics including algebraic geometry, complex analysis, differential geometry, topology and mathematical physics. The present project investigated these moduli spaces and modular groups, mainly form the point of view of topology, and obtained many interesting results. Furthermore, we obtained new results as well as conjectures in the closely related theories of 3 and 4 dimensional manifolds and transversely symplectic foliations. We also proposed a deep problem towards new directions of our research including number theory.
期刊论文(22)
专著(0)
科研奖励(0)
会议论文
The Magnus representation and higher-order Alexander invariants for homology cobordisms of surfaces
曲面同源配边的马格努斯表示和高阶亚历山大不变量
DOI: --
发表时间: 2008
期刊: Algebraic&Geometric Topology
影响因子: --
作者: [A. Adare, T. Gunji, et. al. (for the PHENIX Collaboration), T. Gunji, Masataka Chida, Masataka Chida, Masataka Chida, Takuya Sakasai]
通讯作者: Takuya Sakasai
DOI: --
发表时间: 2008
期刊:
影响因子: --
作者: [Maruyama R., et al., 森田茂之]
通讯作者: 森田茂之
DOI: --
发表时间: 2009
期刊:
影响因子: --
作者: [Mikiya Masuda, Dong Youp Suh, 森田茂之]
通讯作者: 森田茂之
A Partial Order in the Knot Table II
结表 II 中的偏序
DOI: --
发表时间: 2008
期刊: Acta Mathematica Sinica 24
影响因子: --
作者: [S.Akiyama, J.Thuswaldner, K.Hikami, 樋上 和弘, 高田 敏恵, T.Takata, Teruaki KITANO and Masaaki SUZUKI]
通讯作者: Teruaki KITANO and Masaaki SUZUKI
19
    Geometry of Groups and Moduli Spaces
    • 批准号:
      16204005
    • 项目类别:
      Grant-in-Aid for Scientific Research (A)
    • 资助金额:
      $10.48万
    • 财政年份:
      2004
    • 负责人:
      MORITA Shigeyuki
    • 依托单位:
    Mapping Class Group of Surfaces and Geometry of Moduli Spaces
    • 批准号:
      13440017
    • 项目类别:
      Grant-in-Aid for Scientific Research (B)
    • 资助金额:
      $4.86万
    • 财政年份:
      2001
    • 负责人:
      MORITA Shigeyuki
    • 依托单位:
    STRUCTURE OF THE MAPPING CLASS GROUP AND GEOMETRY OF THE MODULI SPACE OF RIEMANN SURFACES
    • 批准号:
      10440016
    • 项目类别:
      Grant-in-Aid for Scientific Research (B).
    • 资助金额:
      $5.18万
    • 财政年份:
      1998
    • 负责人:
      MORITA Shigeyuki
    • 依托单位:
    COMPREHENSIVE STUDY OF TOPOLOGY
    • 批准号:
      08304006
    • 项目类别:
      Grant-in-Aid for Scientific Research (A)
    • 资助金额:
      $12.61万
    • 财政年份:
      1996
    • 负责人:
      MORITA Shigeyuki
    • 依托单位:
    海外基金