3次元多様体の幾何と基本群

3 维流形和基本群的几何

• 批准号: 06302003
• 负责人: 小島 定吉
• 金额: $ 0.96万
• 依托单位: Tokyo Institute of Technology
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Co-operative Research (A)
• 财政年份: 1994
• 资助国家: 日本
• 起止时间: 1994 至 无数据
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-06302003/
• 关键词: 3次元多様体; 双曲多様体; 幾何構造; 基本群

最近の3次元多様体論の成果を概観し,今後の研究方向について色々な角度から討論をおこなうため,東京工業大学で12月19日より4日間のべ150名の参加者を集め「3次元多様体論」と題した研究集会を開催した.午前中は北野晃朗(東工大)が中心になり,接触構造,カット&ペースト,写像類群に関する最近の成果についてサーベイを行った.午後は分担者と小林穀(奈良女子大)がそれぞれ座長を勤める5つの特別セッションを催した.森田茂之は,河野俊丈(東大)・深谷賢治(京大)・村上順(阪大)・N.Reshetikhin(Berkeley)の各氏の講演を集め,無限次元を経由して得られる3次元多様体の位相不変量についての研究の最近の展開を網羅した.吉田朋好は,松本幸夫(東大)・高倉樹(福岡大)・橋本義武(阪市大)の各氏の講演を集め,リーマン面の研究との係わりの重要性を強調した.神島芳宣は,D.McCullough(Oklahoma)・S.Hong(Pusan)の両氏を講演に招き,3次元多様体の写像類群に関する米国での研究の展開を紹介した.相馬輝彦は,大鹿健一氏(東工大)と共同で,不連続群論と3次元多様体論という2つの分野の相互作用の最近の展開とその魅力を,トポロジスト向けに概観した.小林穀は,作間誠(阪大)・D.Heath(奈良女子大)の両氏と共に,Heegaard分野に関する最近の興味深い成果を挙げ,古典的な手法の有用性を披露した.やや発散気味の研究集会となったが,多数の参加者を集め充実した討論ができた.今後の研究方向について答えは1つではないが,重要な問題と進むべき方向がいくつか示唆され,当初の目的は達成できたといえる.

An overview of the results of the third-dimensional multi-body theory has been published recently. in the future, the research direction will be held in the future. On December 19, Beijing University of Technology held a seminar for 150 participants to hold a research meeting on the topic of "three-dimensional multi-body theory". In the middle of the afternoon, the center of Kitano Kuo Lang ("University of Technology)" will be contacted, and the writing group will be in contact with the latest results. The afternoon attendant, Kobayashi Kobayashi (Nara Women's University), is very diligent and special to urge you to do so. Shigeru Morita, Toshihiro Kono (Kono) Shunji Kono (Peking University), Murakami (Sakakami) N.Reshetikhin (Berkeley) has performed a series of performances, and the limited-order multi-dimensional multi-dimensional phase has recently been launched in the Internet. Yukio Yoshida, Yukio Matsumoto, Yukio Matsumoto, Takeshi Matsumoto, Takeshi Takeshi, Takeshi Koji, Yoshimoto Yoshida, Yoshida Yoshida, Yoshida Yoshida, Yukuo Matsumoto, Yukio Matsumoto, Yukuo Matsumoto, Yukio Matsumoto, Takeshi Matsumoto, Takes Shenmu Fang Xuan, D.McCullough (Oklahoma) S.Hong (Pusan), the third-dimensional multi-body writing group, the United States, the United States, and the study of the United States. Each other, the deer Jianyi (University of Technology) "common", do not link the group discussion "3-dimensional multi-dimensional body theory", "2", "field" interaction "recently", "charm", "charm" to "overview". Kobayashi Kobayashi, D.Heath (Nara Women's University), Kobayashi Kobayashi, D.Heath, Nara, Nara, Kobayashi, Hanaka, Nara, Nara, Kobayashi, Kobayash Most of the participants gathered at the research meeting to discuss and discuss the situation. In the future, the direction of the research will answer the question of the first time, and the direction of the progress of the important questions will show that they are instigated. At the beginning, the purpose has become the goal.

项目成果

S.KOJIMA: "Geometry of hyperbolic 3-manitolds with boundary" Kodai Math.J.17. 530-537 (1994)

S.KOJIMA：“具有边界的双曲 3-manitold 的几何”Kodai Math.J.17。

T.SOMA: "A rigidity theorem for Haken manifolds" Math.Proc Camb.Phil.Soc.(発表予定).

T.SOMA：“Haken 流形的刚性定理”Math.Proc Camb.Phil.Soc。

Y.KAMISHIMA: "Standard psends-Hermitian structve and Seifertfibration on CR manifolds" Ann.of Global Analysis and Geometry. 12. 261-289 (1994)

Y.KAMISHIMA：“CR 流形上的标准 pends-Hermitian 结构和 Seifertfibration”Ann.of Global Analysis and Geometry。

S.MORITA: "Charactevistic classes of surtace bundles and the Casson inyariant" Sugaku Exposition. 7. 59-79 (1994)

S.MORITA：“表面丛的特征类别和 Casson inyariant”Sugaku 阐述。

Y.KAMISHIMA: "Uniformigation of Kahler manifolds with vanishing Bochuer tensor" Acta Math.172. 299-308 (1994)

Y.KAMISHIMA：“卡勒流形与消失的 Bochuer 张量的统一”Acta Math.172。