Study of homotopical properties of Lie groups

2008 Fiscal Year Self-evaluation Report

• Project/Area Number: 18540064
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Ibaraki University
• Principal Investigator: OSHIMA Hideaki Ibaraki University, 理学部, 教授 (70047372)
• Project Period (FY): 2006 – 2009
• Keywords: リー群 / ホモトピー

Research Abstract

リー群をホモトピー的側面から研究する.特にリー群Gの連続自己写像を主に研究する :
(1) Gの自己連続写像のホモトピー類群H(G)の解析.
(2) Gの連続自己写像全体のなす位相空間map(G,G)のホモトピー群の計算.
(3) Gの自己ホモトピー同値写像のホモトピー類群E(G)と関連する群の計算.
(4) 単連結単純リー群の圏から群の圏への関手H, E が忠実であるか否か,否の場合にはその度合いを決定する.

Research Products

• [Journal Article] Homotopy groups of the spaces of self-maps of Lie groups (2008)
  • Author(s): Ken-ichi Maruyama and Hideaki Oshima
  • Journal Title: J. Math. Soc. Japan 60 Pages: 767-792
  • Peer Reviewed
• [Journal Article] A quotient group of the group of self homotopy equivalences of SO(4) (2008)
  • Author(s): Hideaki Oshima
  • Journal Title: Kodai Math. J. 31 Pages: 82-91
  • Peer Reviewed
• [Journal Article] Notes on operator categories (2007)
  • Author(s): Shigeru Yamagami
  • Journal Title: J. Math. Soc. Japan 59 Pages: 541-555
  • Peer Reviewed
• [Journal Article] Homotopy classes of self-maps and induced homomorphisms of homotopy groups (2006)
  • Author(s): Martin Arkowitz, Jeffrey Strom and Hideaki Oshima
  • Journal Title: J. Math. Soc. Japan 58 Pages: 401-418
  • Peer Reviewed
• [Presentation] Homotopy classes of self maps (2006)
  • Author(s): Hideaki Oshima
  • Organizer: International Conference on Algebraic Topology
  • Place of Presentation: Henan University
  • Year and Date: 2006-10-15