Study of Hopf spaces by using higher order cohomology operations

• Project/Area Number: 23540093
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kochi University
• Principal Investigator: HEMMI Yutaka 高知大学, 教育研究部自然科学系, 教授 (70181477)
• Co-Investigator(Kenkyū-buntansha): KAWAMOTO Yusuke 防衛大学校, 総合教育学群, 准教授 (10531759) ; MORISUGI Kaoru 和歌山大学, 教育学部, 特任教授 (00031807) ; YAMAGUCHI Toshihiro 高知大学, 教育研究部自然科学系, 教授 (90346700)
• Project Period (FY): 2011 – 2013
• Project Status: Completed (Fiscal Year 2013)
• Budget Amount: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000); Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2011: ¥2,340,000 (Direct Cost: ¥1,800,000、Indirect Cost: ¥540,000)
• Keywords: 非安定高位コホモロジー作用素 / ホップ空間 / 高位ホモトピー結合性 / Long Toda積 / cyclohedron / 高位ホモトピー可換性 / コホモロジー作用素 / 有限位相空間 / 有限単体的複体 / 配置空間 / 実射影空間 / 安定拡張可能 / 有理ホモトピー / Gottlieb群

Research Abstract

It is known that the non trivial p-component of the homotopy group of 2n+1 dimensional sphere occurs in dimension 2n+2i(p-1)-1 for n<i<p. The generators for the case of n=1 is given by the composition of the Toda's alpha elements, but for n>1 we showed that they are given by the Toda bracket or higher Toda brackets. We studied higher cohomology operatons detecting these generators. For 3-sphere we showed that it is the secoandary operation which has been useful in studying higher homotopy associativity of Hopf spaces

Research Products

• [Journal Article] C-symplectic poset structure on a simply connected space (2014)
  • Author(s): Kazuya Hamada, Toshihiro Yamaguchi and Shoji Yokura
  • Journal Title: Topology and its Applications Volume: 161 Pages: 107-126
  • DOI: 10.1016/j.topol.2013.09.009
  • Peer Reviewed
• [Journal Article] Stable extendibility of vector bundles over real projective spaces (2013)
  • Author(s): Y. Hemmi and T. Kobayashi
  • Journal Title: Topology Appl Volume: 160巻 Pages: 2170-2174
  • Peer Reviewed
• [Journal Article] Higher homotopy commutativity of H-spaces and the cyclohedra (2013)
  • Author(s): Y. Kawamoto
  • Journal Title: Publ. Res. Inst. Math. Sci Volume: 49巻 Pages: 737-760
  • Peer Reviewed
• [Journal Article] Pre-c-symplectic condition for the product of odd-spheres (2013)
  • Author(s): J. Sato, and T. Yamaguchi
  • Journal Title: J. Homotopy Relat. Struct Volume: 8巻 Pages: 13-34
  • Peer Reviewed
• [Journal Article] Certain homotopy subgroups associated with a map (2013)
  • Author(s): T. Yamaguchi
  • Journal Title: Kochi J. Math Volume: 8巻 Pages: 35-45
  • Peer Reviewed
• [Journal Article] C-symplectic poset structure on a simply connected space (2013)
  • Author(s): K. Hamada, T. Yamaguchi and S. Yokura
  • Journal Title: Topology Appl Volume: 161巻 Pages: 107-126
  • Peer Reviewed
• [Journal Article] Stable extendibility of vector bundles over real projective spaces (2013)
  • Author(s): Y. Hemmi and T. Kobayashi
  • Journal Title: Topology Appl. Volume: 160 Issue: 17 Pages: 2170-2174
  • DOI: 10.1016/j.topol.2013.09.001
  • Peer Reviewed
• [Journal Article] Higher homotopy commutativity of H-spaces and the cyclohedra (2013)
  • Author(s): Y. Kawamoto
  • Journal Title: Publ. Res. Inst. Math. Sci. Volume: 49 Issue: 4 Pages: 737-760
  • DOI: 10.4171/prims/118
  • Peer Reviewed
• [Journal Article] Pre-c-symplectic condition for the product of odd-spheres (2013)
  • Author(s): J. Sato and T. Yamaguchi
  • Journal Title: Homotopy Relat. Struct. Volume: 8 Issue: 1 Pages: 13-34
  • DOI: 10.1007/s40062-012-0011-6
  • Peer Reviewed
• [Journal Article] Certain homotopy subgroups associated with a map (2013)
  • Author(s): T. Yamaguchi
  • Journal Title: Kochi J. of Math. Volume: 8 Pages: 35-45
  • Peer Reviewed
• [Journal Article] Pre-c-symplectic condition for the product of odd-spheres (2013)
  • Author(s): J. Sato, and T. Yamaguchi
  • Journal Title: J. Homotopy Relat. Struct. Volume: 8巻 Pages: 13-34
  • Peer Reviewed
• [Journal Article] The closed chains with spherical configulation spaces (2012)
  • Author(s): S. Goto, Y. Hemmi, K. Komatsu and J. Yagi
  • Journal Title: Hiroshima Math J Volume: 42巻 Pages: 253-266
  • Peer Reviewed
• [Journal Article] Examples of rational toral rank complex (2012)
  • Author(s): T. Yamaguchi
  • Journal Title: Int. J. Math. Sci Volume: 2012巻
  • Peer Reviewed
• [Journal Article] The closed chains with spherical configulation spaces (2012)
  • Author(s): S. Goto, Y. Hemmi, K. Komatsu and J. Yagi
  • Journal Title: Hiroshima Math J. Volume: 42巻 Pages: 253-266
  • Peer Reviewed
• [Journal Article] Examples of rational toral rank complex (2012)
  • Author(s): T. Yamaguchi
  • Journal Title: Int. J. Math. Sci. Volume: 2012巻 Pages: 1-8
  • Peer Reviewed
• [Journal Article] Higher homotopy commutativity and the resultohedra (2011)
  • Author(s): Y. Hemmi and Y. Kawamoto
  • Journal Title: J. Math. Soc. Japan Volume: 63巻 Pages: 443-471
  • NAID: 10029321602
  • Peer Reviewed
• [Journal Article] A Hasse diagram for rational toral ranks (2011)
  • Author(s): T. Yamaguchi
  • Journal Title: Bull. Belg. Math. Soc. Simon Stevin Volume: 18巻 Pages: 493-508
  • Peer Reviewed
• [Journal Article] Examples of a Hasse diagram of free circle actions in rational homotopy (2011)
  • Author(s): T. Yamaguchi
  • Journal Title: JP Journal of Geometry and Topology Volume: 11巻 Pages: 181-191
  • Peer Reviewed
• [Presentation] 有限位相空間における連続写像の拡張とホモトピーについて (2013)
  • Author(s): 板垣早紀, 逸見豊
  • Organizer: 高知ホモトピー論セミナー
  • Place of Presentation: 高知大学(高知県)
  • Year and Date: 2013-12-16
• [Presentation] Higher homotopy associativity of power mapson finite H-spaces (2013)
  • Author(s): 河本裕介
  • Organizer: 高知ホモトピー論セミナー
  • Place of Presentation: 高知大学(高知県)
  • Year and Date: 2013-12-16
• [Presentation] Higher homotopy associativity of power mapson finite H-spaces (2013)
  • Author(s): 河本裕介
  • Organizer: ホモトピー論シンポジウム
  • Place of Presentation: 岡山大学(岡山県)
  • Year and Date: 2013-11-04
• [Presentation] 有限位相空間の圏と有限単体的複体の圏の対応について (2013)
  • Author(s): 板垣早紀, 逸見豊
  • Organizer: ホモトピー論シンポジウム
  • Place of Presentation: 岡山大学(岡山県)
  • Year and Date: 2013-11-02
• [Presentation] ホップ空間の高位ホモトピー可換性と巡回多面体 (2013)
  • Author(s): 河本裕介
  • Organizer: 日本数学会, 2013年度年会トポロジー分科会
  • Place of Presentation: 京都大学(京都府)
  • Year and Date: 2013-03-22
• [Presentation] 詰め込み複体vs トーラス階数複体 (2013)
  • Author(s): 山口俊博
  • Organizer: 鹿児島大学数理情報科学さくらセミナー
  • Place of Presentation: 鹿児島大学(鹿児島県)
  • Year and Date: 2013-03-18
• [Presentation] いくつかの不変量に潜む図形の観察 (2013)
  • Author(s): 山口俊博
  • Organizer: 高知大学理学部門談話会
  • Place of Presentation: 高知大学(高知県)
  • Year and Date: 2013-01-23
• [Presentation] The topology of a model for ringed hydrocarbon molecules (2012)
  • Author(s): 八木潤, 後藤了, 小松和志, 逸見豊
  • Organizer: 日本数学会, 秋季総合分科会
  • Place of Presentation: 九州大学(福岡県)
  • Year and Date: 2012-09-21
• [Presentation] 有理トーラス階数達が張るCW複体 (2012)
  • Author(s): 山口俊博
  • Organizer: 鹿児島大学数理情報科学談話会
  • Place of Presentation: 鹿児島大学(鹿児島県)
  • Year and Date: 2012-06-01
• [Presentation] 写像の高位ホモトピー可換性について (2012)
  • Author(s): 河本裕介
  • Organizer: 福岡ホモトピー論セミナー
  • Place of Presentation: 福岡大学(福岡県)
  • Year and Date: 2012-01-07
• [Presentation] 写像の高位ホモトピー可換性について (2012)
  • Author(s): 河本裕介
  • Organizer: 福岡ホモトピー論セミナー
  • Place of Presentation: 福岡大学（福岡県）
• [Presentation] The topology of a model for ringed hydrocarbon molecules
  • Author(s): 八木，後藤，小松，逸見
  • Organizer: 日本数学会，秋季総合分科会
  • Place of Presentation: 九州大学（福岡県）
• [Presentation] ホップ空間の高位ホモトピー可換性と巡回多面体
  • Author(s): 河本裕介
  • Organizer: 日本数学会，2013年度年会トポロジー分科会
  • Place of Presentation: 京都大学（京都府）
• [Presentation] 有理トーラス階数達が張るCW複体
  • Author(s): 山口俊博
  • Organizer: 鹿児島大学数理情報科学談話会
  • Place of Presentation: 鹿児島大学（鹿児島県）
• [Presentation] いくつかの不変量に潜む図形の観察
  • Author(s): 山口俊博
  • Organizer: 高知大学理学部門談話会
  • Place of Presentation: 高知大学（高知県）
• [Presentation] 詰め込み複体vsトーラス階数複体
  • Author(s): 山口俊博
  • Organizer: 鹿児島大学数理情報科学さくらセミナー
  • Place of Presentation: 鹿児島大学（鹿児島県）