Study of the topological structure of metric spaces of non-positive curvature

• Project/Area Number: 18740023
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: University of Tsukuba (2007-2008); Tohoku University (2006)
• Principal Investigator: NAGANO Koichi University of Tsukuba, 大学院・数理物質科学研究科, 講師 (30333777)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,830,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥330,000); Fiscal Year 2008: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000); Fiscal Year 2006: ¥1,300,000 (Direct Cost: ¥1,300,000)
• Keywords: 微分幾何学 / リーマン幾何学 / 幾何学 / CAT(0)空間 / アダマール空間 / アレキサンドルフ空間 / CAT(1)空間 / アレキサンドロフ空間

Research Abstract

研究成果の概要 : 非正曲率距離空間に代表されるCAT(k)空間の位相構造の理解を目指し,主に,CAT(k)空間がいつn次元位相多様体になるかについて記述する局所位相正則性の問題(Lytchak氏と共同),および2次元CAT(k)空間の幾何構造と位相構造に関するGauss・Bonnetの定理等(Kleiner氏,塩谷氏,山口氏と共同)について取り組み,汎用性の高い成果を得た.

Research Products

• [Journal Article] Free construction of CAT(1) spaces (2007)
  • Author(s): Koichi Nagano
  • Journal Title: Archiv der Mathematik 88 Pages: 173-180
  • Peer Reviewed
• [Journal Article] Free construction of CAT(1)spaces (2007)
  • Author(s): Koichi Nagano
  • Journal Title: Archiv der Mathematik 88 Pages: 173-180
  • Peer Reviewed
• [Journal Article] Fixed point sets of parabolic isometries of CAT(0)-spaces (2006)
  • Author(s): Koji Fujiwara, Koichi Nagano, and Takashi Shioya
  • Journal Title: Commentarii Mathematici Helvetici 81 Pages: 305-335
  • Peer Reviewed
• [Presentation] 曲率が上に有界な2次元距離空間 (2008)
  • Author(s): 永野幸一
  • Organizer: 東北大学談話会
  • Place of Presentation: 東北大学
  • Year and Date: 2008-11-17
• [Presentation] 曲率が上に有界な2次元距離空間 (2008)
  • Author(s): 永野幸一
  • Organizer: 東北大学談話会
  • Place of Presentation: 東北大学川井ホール
  • Year and Date: 2008-11-17
• [Presentation] A characterization of 2-dimensional spherical buildings (2008)
  • Author(s): 永野幸一
  • Organizer: 研究会「リーマン幾何と幾何解析」
  • Place of Presentation: 筑波大学
  • Year and Date: 2008-02-19
• [Presentation] A characterization of 2-dimensional spherical buildings (2008)
  • Author(s): 永野幸一
  • Organizer: リーマン幾何と幾何解析
  • Place of Presentation: 筑波大学
  • Year and Date: 2008-02-19
• [Presentation] Topological regularity of Alexandrov spaces with an upper curvature bound (2007)
  • Author(s): Koichi Nagano
  • Organizer: Third Russian-German Geometry Meeting-dedicated 95-anniversary of A. D. Alexandrov
  • Place of Presentation: Steklov Institute of Mathematics (St. Petersburg, Russia)
  • Year and Date: 2007-06-18
• [Presentation] Topological regularity of Alexandrov spaces with an upper curvature bound (2007)
  • Author(s): Koichi, Nagano
  • Organizer: Third Russian-German Geometry Meeting-dedicated 95-anniversary of A.D.Alexandrov
  • Place of Presentation: Steklv Institute of Math.(St.Petersburg,Russia)
  • Year and Date: 2007-06-18
• [Presentation] CAT(1)空間の位相正則性 (2006)
  • Author(s): 永野幸一
  • Organizer: 東北大学談話会
  • Place of Presentation: 東北大学
  • Year and Date: 2006-12-18
• [Presentation] CAT(1)空間の求積可能性 (2006)
  • Author(s): 永野幸一
  • Organizer: 研究会「測地線及び関連する諸問題」,
  • Place of Presentation: 熊本大学
  • Year and Date: 2006-10-28
• [Presentation] Topological regularity of CAT(1) spaces (2006)
  • Author(s): Koichi Nagano
  • Organizer: Rigidity School, Nagoya 2006
  • Place of Presentation: 名古屋大学
  • Year and Date: 2006-09-28
• [Presentation] A sphere theorem for CAT(1) spaces (2006)
  • Author(s): 永野幸一
  • Organizer: 日本数学会秋期総合分科会幾何学分科会, 特別講演
  • Place of Presentation: 大阪市立大学
  • Year and Date: 2006-09-21
• [Presentation] Topological regularity of CAT(1) spaces (2006)
  • Author(s): 永野幸一
  • Organizer: 第53回幾何学シンポジウム,全体講演
  • Place of Presentation: 金沢大学
  • Year and Date: 2006-08-05
• [Presentation] Topological regularity of CAT(1) spaces (2006)
  • Author(s): 永野幸一
  • Organizer: 岡山大学談話会
  • Place of Presentation: 岡山大学
  • Year and Date: 2006-07-21
• [Presentation] Distance and convexity (2006)
  • Author(s): Koichi Nagano
  • Organizer: 第4回COEシンポジウム「物質階層融合科学の構築」国際会議
  • Place of Presentation: 仙台国際センター
  • Year and Date: 2006-06-28
• [Presentation] Topological regularity of CAT(1) spaces (2006)
  • Author(s): 永野幸一
  • Organizer: 筑波大学微分幾何学火曜セミナー
  • Place of Presentation: 筑波大学
  • Year and Date: 2006-06-27
• [Presentation] Rectifiability of CAT(1) spaces (2006)
  • Author(s): 永野幸一
  • Organizer: 東北大学幾何学セミナー
  • Place of Presentation: 東北大学
  • Year and Date: 2006-04-25