Applications of homotopy algebras to geometry and its deformation problems

• Project/Area Number: 19740038
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Geometry
• Research Institution: Chiba University (2008-2009); Kyoto University (2007)
• Principal Investigator: KAJIURA Hiroshige Chiba University, 大学院・理学研究科, 准教授 (30447891)
• Project Period (FY): 2007 – 2009
• Project Status: Completed (Fiscal Year 2009)
• Budget Amount: ¥3,700,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥600,000); Fiscal Year 2009: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000); Fiscal Year 2007: ¥1,100,000 (Direct Cost: ¥1,100,000)
• Keywords: 幾何学 / トポロジー / 代数学 / 数理物理 / 素粒子論 / ホモトピー代数 / 位相的弦理論 / Dブレイン / 三角圏 / 複素構造

Research Abstract

We studied Fukaya categories which are categories consisting of Lagrangian submanifolds in symplectic manifolds. We constructed an A-infinity structure in the Fukaya category of lines in a plane completely and explicitly. Also, we studies relations between A-infinity categories and triangulated categories which are general tools to describe geometry. We constructed an example of triangulated categories whose A-infinity enhancements are not unique.

Research Products

• [Journal Article] An A-infinity structure for lines in a plane (2009)
  • Author(s): Hiroshige Kajiura
  • Journal Title: International Mathematical Research Notices 20巻 Pages: 3913-3955
  • Peer Reviewed
• [Journal Article] Triangulated categories of matrix factorizations for regular systems of weights withε=-1 (2009)
  • Author(s): Hiroshige Kajiura, Kyoji Saito, Atsushi Takahashi
  • Journal Title: Advances in Mathematics 220巻 Pages: 1602-1654
  • Peer Reviewed
• [Journal Article] An A-infinity structure for lines in a plane (2009)
  • Author(s): Hiroshige Kajiura
  • Journal Title: International Mathematical Research Notices No.20 Pages: 3913-3955
  • Peer Reviewed
• [Journal Article] Triangulated categories of matrix factorizations for regular systems of weights (2009)
  • Author(s): Hiroshige Kajiura, et.al.
  • Journal Title: Advances in Mathematics 220 Pages: 1602-1654
  • Peer Reviewed
• [Journal Article] Homotopy algebra of open-closed strings (2008)
  • Author(s): Hiroshige Kajiura, Jim Stasheff
  • Journal Title: Geometry & Topology Monographs 13巻 Pages: 229-259
  • Peer Reviewed
• [Journal Article] Homotopy algebra of open-closed strings (2008)
  • Author(s): Hiroshige Kajiura, Jim Stasheff
  • Journal Title: Geometry & Topology Monographs 13 Pages: 229-259
  • Peer Reviewed
• [Journal Article] String theory and deformation quantization (2007)
  • Author(s): Yoshiaki Maeda, Hiroshige Kajiura
  • Journal Title: ugaku expositions 20巻 Pages: 191-214
• [Journal Article] String theory and deformation quantization (2007)
  • Author(s): Yoshiaki Maeda, Hiroshige Kaiiura
  • Journal Title: Sugaku expositions 20 Pages: 191-214
• [Presentation] On A-infinity enhancements for triangulated categories (2009)
  • Author(s): Hiroshige Kajiura
  • Organizer: Joint meeting of the Korean Mathematical Society and the American Mathematical Society
  • Place of Presentation: Ewha womens university in Seoul, Korea
  • Year and Date: 2009-12-19