unstable K-theory and homotopy-nilpotency of Lie groups

• Project/Area Number: 18740032
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Hyogo University of Teacher Education
• Principal Investigator: HAMANAKA Hiroaki Hyogo University of Teacher Education, 大学院・学校教育研究科, 准教授 (20294267)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,250,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥150,000); Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2007: ¥500,000 (Direct Cost: ¥500,000); Fiscal Year 2006: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: 位相幾何 / ホモトピー論 / リー群 / ホモトピー可換 / 巾零性 / Samelson積 / ホモトピー的巾零性 / ユニタリ群 / トポロジー / ホモトピー / ゲージ群 / K理論 / ユニタリー群

Research Abstract

群という代数的な構造と、図形としての構造を併せ持つリー群では、その代数的な構造を幾何的に考察するという興味深い研究課題が成り立つ。例えばユニタリ群のように行列を要素とする集合の群では、一般に積の順番を入れ替えると結果が変わってしまう(代数的性質 : 非可換性)が、このことは2つの行列AとBに対して、その交換子ABA^<-1>B^<-1>が単位行列にならないことを意味する。しかし個々の行列ではなく、2つの行列から交換子への写像として捉えると、この写像を連続的に変形して常に単位行列になるようにできるかという問題(位相幾何的性質 : ホモトピー可換性)になる。本研究では、ユニタリ群等について、このホモトピー可換性をさらに拡張したホモトピー巾零性について研究した。

Research Products

• [Journal Article] Samelson products in Sp(2) (2008)
  • Author(s): 濱中 裕明、鍛冶 静雄、河野 明
  • Journal Title: Topology and its Applications No. 155 Pages: 1207-1212
  • Peer Reviewed
• [Journal Article] Samelson products in Sp(2) (2008)
  • Author(s): 濱中裕明、鍛冶静雄、河野明
  • Journal Title: Topology and its Applications 155 Pages: 1207-1212
  • Peer Reviewed
• [Journal Article] Homotopy type of gauge groups of SU(3)-bundles over S^6 (2007)
  • Author(s): 濱中 裕明、河野明
  • Journal Title: Topology and its Applications No. 154 Pages: 1377-1380
  • Peer Reviewed
• [Journal Article] Nilpotency of unstable K-theory (2007)
  • Author(s): 濱中 裕明
  • Journal Title: Topology and its Applications No. 154 Pages: 1368-1376
  • Peer Reviewed
• [Journal Article] A note on the Samelson product in p*(SO(2n)) and the group [SO(2n), SO(2n)] (2007)
  • Author(s): 濱中 裕明、河野明
  • Journal Title: Topology and its Applications No. 154 Pages: 567-572
  • Peer Reviewed
• [Journal Article] On Samelson product in p-localized unitary groups (2007)
  • Author(s): 濱中 裕明
  • Journal Title: Topology and its Applications No. 154 Pages: 578-583
  • Peer Reviewed
• [Journal Article] Nilpotency of unstable K- theory (2007)
  • Author(s): 濱中 裕明
  • Journal Title: Topology and its Applications 154 Pages: 1368-1376
  • Peer Reviewed
• [Journal Article] Homotopy type of gauge groups of SU(3)-bundles over S6 (2007)
  • Author(s): 濱中 裕明(共著)
  • Journal Title: Topology and its Applications 154 Pages: 1377-1380
  • Peer Reviewed
• [Journal Article] On Samelson product in p-localized unitary groups (2007)
  • Author(s): 濱中 裕明 (共著)
  • Journal Title: Topology and its Applications 154 Pages: 578-583
• [Journal Article] A note on the Samelson product in π *(SO(2n)) and the group [SO(2n),SO(2n)] (2007)
  • Author(s): 濱中 裕明 (共著)
  • Journal Title: Topology and its Applications 154 Pages: 567-572
• [Journal Article] Unstable K1-group and homotopy type of certain gauge groups (2006)
  • Author(s): 濱中 裕明、河野明
  • Journal Title: Proceedings of the Royal Society of Edinburgh No. 136A Pages: 149-155
  • Peer Reviewed
• [Journal Article] Self homotopy groups with large Nilpotency classes (2006)
  • Author(s): 濱中 裕明、岸本大祐、河野明
  • Journal Title: Topology and its Applications No. 153 Pages: 2425-2429
  • Peer Reviewed
• [Journal Article] Self homotopy groups with large Nilpotency classes (2006)
  • Author(s): 濱中 裕明 (共著)
  • Journal Title: Topology and its Applications 153 Pages: 2425-2429
• [Journal Article] Unstable K1-group and homotopy type of certain gauge groups (2006)
  • Author(s): 濱中 裕明 (共著)
  • Journal Title: Proceedings of the Royal Society of Edinburgh 136A Pages: 149-155
• [Presentation] Samelson products in π*(U(n)) in the meta-stable range (2008)
  • Author(s): 濱中 裕明
  • Organizer: ホモトピー論シンポジウム
  • Place of Presentation: 高松
  • Year and Date: 2008-12-06
• [Presentation] Samelson products in π*(U(n)) in the meta-stable range (2008)
  • Author(s): 濱中裕明
  • Organizer: ホモトピー論シンポジウム
  • Place of Presentation: サンポートホール高松(香川)
  • Year and Date: 2008-12-06
• [Presentation] p-localized unstable K-theory with nilpotency class 3 (2006)
  • Author(s): 濱中 裕明
  • Organizer: International Conference on Algebraic Topology
  • Place of Presentation: 中国/河南大学
  • Year and Date: 2006-10-16