Reconstruction of 2 and 3-dimensional closed manifolds by equi-dimensional stable maps and classification of embedding or immersion lifts

• Project/Area Number: 25800032
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Hirosaki University
• Principal Investigator: Yamamoto Minoru 弘前大学, 教育学部, 准教授 (40435475)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000); Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
• Keywords: 安定折り目写像 / はめ込み / レンズ空間 / ヒーガード分解 / 3次元閉多様体 / はめ込みリフト / コボルダント / 安定な折り目写像 / 向き付け可能な3次元閉多様体 / モース型の不等式 / はめ込みの拡張 / 折り目写像

Outline of Final Research Achievements

The research leader studied constructions of stable fold maps of closed oriented 3-dimensional manifolds to the 3-space and lifts of these stable fold maps to immersions to the 4-space. The research results are as follows. (1): The leader constructed stable fold map of the lens space L(p, 1) to the 3-space whose singularity set is a torus. (2): The leader showed that an immersion lift of the stable fold map of the 3-sphere which was constructed in (1) to the 4-space is a generator of the cobordism group of the closed oriented 3-dimensional manifold to the 4-space.

Research Products

• [Journal Article] Views of real projective 3-space by stable maps into the plane (2017)
  • Author(s): Mahito Kobayashi, Minoru Yamamoto
  • Journal Title: Experimental Mathematics Volume: 26 Issue: 2 Pages: 138-152
  • DOI: 10.1080/10586458.2016.1142910
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] 三角数の交代和による表示と高次元化 (2016)
  • Author(s): 田中義久，山本稔
  • Journal Title: 日本数学教育学会誌数学教育70-2 Volume: 98 Pages: 3-10
  • NAID: 130007936105
  • Peer Reviewed
• [Journal Article] On embedding lifts over a Morse function on a circle (2013)
  • Author(s): Minoru Yamamoto
  • Journal Title: RIMS Kokyuroku Bessatsu Volume: B38 Pages: 31-43
  • Peer Reviewed
• [Presentation] 3次元兵多様体から3次元空間への折り目写像の構成について (2016)
  • Author(s): 山本稔
  • Organizer: 特異点の大域的研究
  • Place of Presentation: 兵庫教育大学神戸ハーバーランドキャンパス
• [Presentation] Construction of fold map of lens space L(p,1) where singular set is a torus (2016)
  • Author(s): Minoru Yamamoto
  • Organizer: Singularity theory of differential maps and its applications
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] Stable fold maps of oriented 3-manifolds to 3-space (ポスター発表) (2015)
  • Author(s): Minoru Yamamoto
  • Organizer: Singularities in Generic Geometry and its applications --Kobe-Kyoto 2015 (Valencia IV)--
  • Place of Presentation: 神戸大学
  • Year and Date: 2015-06-05
  • Int'l Joint Research
• [Presentation] トーラスを折り目とする3次元球面から3次元空間への折り目写像の構成法について (2014)
  • Author(s): 山本稔
  • Organizer: 研究集会「多様体のトポロジーの展望」
  • Place of Presentation: 東京大学大学院数理科学研究科
  • Year and Date: 2014-11-29
• [Presentation] Extension of immersed circles in the plane to a surface (Introduction of the works of Blank and Francis) (2014)
  • Author(s): 山本稔
  • Organizer: Kobe Studio Seminar for Studies with Renderman
  • Place of Presentation: 神戸大学
  • Year and Date: 2014-10-25
• [Funded Workshop] Singularities in Generic Geometry and its applications --Kobe-Kyoto 2015 (Valencia IV)-- (2015)
  • Place of Presentation: 神戸大学，京都大学数理解析研究所
  • Year and Date: 2015-06-03