Local and global structures in homotopy theory

• Project/Area Number: 18740031
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: KISHIMOTO Daisuke Kyoto University, 大学院・理学研究科, 准教授 (60402765)
• Project Period (FY): 2006 – 2009
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,070,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥270,000); Fiscal Year 2008: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); Fiscal Year 2007: ¥900,000 (Direct Cost: ¥900,000); Fiscal Year 2006: ¥1,000,000 (Direct Cost: ¥1,000,000)
• Keywords: 幾何学 / トポロジー

Research Abstract

空間を局所化して得られる性質に関して, 非単連結なリー群のmod p分解や, リー群の局所化による積構造の変化を研究した. その応用としてあるリー群の自己ホモトピー集合のなす群のベキ零類が非常に大きいことを示した. 空間がもつ局所化に関して不変な性質に関して, 4次元球面上のインスタントンモジュライ空間内の特殊な軌道空間が, Bottによるgenerating varietyの3重ループ空間版や実とシンプレクティックの場合の周期性を与えることを示した.

Research Products

• [Journal Article] Homotopy nilpotency in p-local loop spaces (2009)
  • Author(s): D. Kishimoto and S. Kaji
  • Journal Title: Math. Z. (掲載予定)
  • Peer Reviewed
• [Journal Article] Homotopy nilpotency in localized SU(n), Homology (2009)
  • Author(s): D. Kishimoto
  • Journal Title: Homotopy and Applications (掲載予定)
  • Peer Reviewed
• [Journal Article] Spin structures on instanton moduli spaces (2009)
  • Author(s): Y. Kamiyama and D. Kishimoto
  • Journal Title: Topology and its Applications (掲載予定)
  • Peer Reviewed
• [Journal Article] Homotopy nilpotency in p-regular loop spaces (2009)
  • Author(s): S. Kaji, D. Kishimoto
  • Journal Title: Mathematische Zeitschrift
  • Peer Reviewed
• [Journal Article] Homotopy nilpotency in localized SU(n) (2009)
  • Author(s): D. Kishimoto
  • Journal Title: Homology, Homotopy and Applications 11 Pages: 61-79
  • Peer Reviewed
• [Journal Article] On a conjecture of Oshima (2009)
  • Author(s): A. Kono, D. Kishimoto
  • Journal Title: Topology and its Applications
  • Peer Reviewed
• [Journal Article] Mod p decompositions of non-simply connected Lie groups (2008)
  • Author(s): D. Kishimoto and A. Kono
  • Journal Title: J. Math. Kyoto Univ. 48, no. 1 Pages: 1-5
  • Peer Reviewed
• [Journal Article] Mod p decompositions of non-simply connected Lie groups (2008)
  • Author(s): D. Kishimoto, A Kono
  • Journal Title: Journal of Mathematics of Kyoto University 48巻・1号(未定)
  • Peer Reviewed
• [Journal Article] Samelson products of SO(3) and applications (2007)
  • Author(s): Y. Kamiyama, D. Kishimoto, A. Kono and S. Tsukuda
  • Journal Title: Glasg. Math. J. 49, no. 2 Pages: 405-409
  • Peer Reviewed
• [Journal Article] L-S category of quaternionic Stiefel manifolds (2007)
  • Author(s): D. Kishimoto
  • Journal Title: Topology Appl. 154, no.7 Pages: 1465-1469
  • Peer Reviewed
• [Journal Article] Samelsonproducts of SO(3) and applications (2007)
  • Author(s): Y. Kamiyama, D. Kishimoto, A. Kono, S. Tsukuda
  • Journal Title: Glasgow Mathematical Journal 49 Pages: 405-409
  • Peer Reviewed
• [Journal Article] L-S category of quaternionic Stiefel manifolds (2007)
  • Author(s): D. Kishimoto
  • Journal Title: Topology and its Applications 154 Pages: 1465-1469
  • Peer Reviewed
• [Journal Article] Self homotopy groups with large nilpotency classes (2006)
  • Author(s): H. Hamanaka, D. Kishimoto and A. Kono
  • Journal Title: Topology Appl. 153, no. 14 Pages: 2424-2429
  • Peer Reviewed
• [Journal Article] Topological proof of Bott periodicity and characterization of BR (2006)
  • Author(s): D.Kishimoto
  • Journal Title: Journal of the Mathematical Society of Japan 58・2 Pages: 299-309
  • NAID: 10018381206
• [Journal Article] Self homotopy groups with large nilpotency classes (2006)
  • Author(s): H.Hamanaka, D.Kishimoto, A.Kono
  • Journal Title: Topology and its Applications 153・14 Pages: 2425-2429
• [Journal Article] Samelson products of SO(3) and applications
  • Author(s): Y.Kamiyama, D.Kishimoto, A.Kono, S.Tsukuda
  • Journal Title: Glasgow Mathematical Journal (to appear)