Study on the structure of manifolds by global singularity theory

• Project/Area Number: 18540102
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Kinki University
• Principal Investigator: SAKUMA Kazuhiro Kinki University, 理工学部, 教授 (80270362)
• Project Period (FY): 2006 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥2,590,000 (Direct Cost: ¥2,200,000、Indirect Cost: ¥390,000); Fiscal Year 2008: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000); Fiscal Year 2007: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2006: ¥900,000 (Direct Cost: ¥900,000)
• Keywords: 可微分写像 / 特異点 / 多様体 / 特性類 / トム多項式 / 無限階微分可能写像 / 可微分多様体 / 写像の特異点 / 折り目特異点 / カスプ / 特異点消去の障害類 / 安定スパン / 障害類 / 折り目写像 / カスプ特異点 / 障害理論 / 分類空間

Research Abstract

向き付け不可能な4次元微分可能閉多様体から安定平行化可能な4次元多様体へのジェネリック写像のカスプ特異点を消去するための一次障害類はトム多項式であり、二次障害類は、4次のシュティーフェル・ホイットニー類であることを発見した。定義域が向き付け可能な場合は、カスプ特異点と臍点のトム多項式(2次シュティーフェル・ホイットニー類と1次ボントリャーギン類)が唯一の障害類である。

Research Products

• [Journal Article] Braid groups and topological quatum computing (2008)
  • Author(s): T. Ootsuka, K. Sakuma
  • Journal Title: World Scientific Publ. Pages: 55-89
• [Journal Article] A note on a recursive formula on the Arf-Kervaire invariant (2008)
  • Author(s): K. Sakuma
  • Journal Title: Int. J. Open Problems Compt. Math. vol.1 Pages: 66-70
• [Journal Article] A note on a recursive formula of the Arf-Kervaire invariant (2008)
  • Author(s): Kazuhiro Sakuma
  • Journal Title: Int. J. Open Problems Compt. Math. Vol. 1 Pages: 66-70
  • Peer Reviewed
• [Journal Article] Existence problem for fold maps, JARCS Proceedings (2007)
  • Author(s): K. Sakuma
  • Journal Title: World Scientific Publ. Pages: 342-387
• [Journal Article] Existence problem for fold maps (2007)
  • Author(s): Kazuhiro Sakuma
  • Journal Title: World Scientific Pages: 342-387
  • Peer Reviewed
• [Presentation] A recursive formula of the Arf-Kervaire invariant (2009)
  • Author(s): 佐久間一浩
  • Organizer: 日本数学会春季総合年会、トポロジー分科会
  • Place of Presentation: 東京大学
• [Presentation] A recursive formula of the Arf-Kervaire invariant (2008)
  • Author(s): Kazuhiro Sakuma
  • Organizer: BYU Math Department Colloquim
  • Place of Presentation: Brigham Young Univ.
  • Year and Date: 2008-11-04
• [Presentation] 平方剰余法則とアレキサンダー多項式の特殊値 (2008)
  • Author(s): 佐久間一浩
  • Organizer: トポロジーセミナー
  • Place of Presentation: 九州大学
• [Presentation] A question on the special value of Alexander polynomial (2008)
  • Author(s): K. Sakuma
  • Organizer: KOOKセミナー
  • Place of Presentation: 大阪市立大学
• [Presentation] Obstruction to eliminating singularities (2007)
  • Author(s): R. Sadykov, O. Saeki, K. Sakuma
  • Organizer: 日本数学会春季総合年会、トポロジー分科会、埼玉大学
• [Presentation] Braid groups and topological quantum computing (2007)
  • Author(s): K. Sakuma
  • Organizer: TQC symposium at Kinki University
• [Presentation] Secondary obstruction to eliminating singularities (2007)
  • Author(s): 佐久間 一浩
  • Organizer: 日本数学会
  • Place of Presentation: 東北大学
• [Presentation] Existence problem of fold maps (2006)
  • Author(s): K. Sakuma
  • Organizer: International Singularity Conference at Beijing Chemical Instituteof Technology
  • Place of Presentation: China
• [Presentation] Global Singularity Theory (2006)
  • Author(s): K. Sakuma
  • Organizer: Colloquim Talk in Math. Department of Brigham Young University
  • Place of Presentation: U.S.A.
• [Book] 微分積分学28講 (2009)
  • Author(s): 青木貴史, 大野泰夫, 尾崎学, 佐久間一浩, 中村弥生
  • Publisher: 培風館
• [Book] 線形代数学28講 (2009)
  • Author(s): 青木貴史, 大野泰夫, 尾崎学, 佐久間一浩, 中村弥生
  • Publisher: 培風館