Coarse geometry related to the coarse Baum-Connes conjecture

• Project/Area Number: 16K17595
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Ehime University
• Principal Investigator: Oguni Shin-ichi 愛媛大学, 理工学研究科(理学系), 教授 (00549446)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Project Status: Completed (Fiscal Year 2020)
• Budget Amount: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000); Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
• Keywords: 粗Baum-Connes予想 / 粗凸距離空間 / 粗ホモトピー / 粗コンパクト化 / 双曲性 / 非正曲率性 / 粗幾何学 / 幾何学

Outline of Final Research Achievements

We studied coarse geometry related to the coarse Baum-Connes conjecture. Also we studied geometric group theory which is deeply related to coarse geometry. Actually we introduced coarsely convex spaces and studied them with Tomohiro Fukaya (Tokyo metropolitan university). Also we introduced generalized Gromov products and studied them with Tomohiro Fukaya and Takamitsu Yamauchi (Ehime university). Also we studied acylindrical hyperbolicity of Artin-Tits groups with Motoko Kato (Ehime university).

Academic Significance and Societal Importance of the Research Achievements

粗Baum-Connes予想に関わる粗幾何学について研究を進めた。粗Baum-Connes予想は、Novikov予想など微分トポロジーへの応用があるということ、および、ヒルベルト空間への粗埋め込み可能性や漸近次元の有限性などの粗幾何学における重要な性質の応用先であるということから、幾何学者やトポロジストを中心とした様々な研究者に興味を持たれている。粗幾何学は幾何学的群論とも深く関わり、この観点からの研究も進めた。本研究は粗幾何学にとどまらず、幾何学の進展に寄与するものであったと思われる。

Research Products

• [Journal Article] A coarse Cartan-Hadamard theorem with application to the coarse Baum-Connes conjecture (2020)
  • Author(s): Tomohiro Fukaya, Shin-ichi Oguni
  • Journal Title: Journal of Topology and Analysis Volume: 12(4) Issue: 03 Pages: 857-895
  • DOI: 10.1142/s1793525319500675
  • Peer Reviewed
• [Journal Article] Coarse compactifications and controlled products (2020)
  • Author(s): Tomohiro Fukaya, Shin-ichi Oguni, Takamitsu Yamauchi
  • Journal Title: Journal of Topology and Analysis Volume: online Issue: 04 Pages: 1-26
  • DOI: 10.1142/s1793525321500102
  • Peer Reviewed
• [Journal Article] Acylindrical hyperbolicity of Artin-Tits groups associated to triangle-free graphs and cones over square-free bipartite graphs (2020)
  • Author(s): Motoko Kato, Shin-ichi Oguni
  • Journal Title: Glasgow Mathematical Journal Volume: Published Online Issue: 1 Pages: 1-14
  • DOI: 10.1017/s0017089520000555
  • Peer Reviewed / Open Access
• [Journal Article] On coarse geometric aspects of Hilbert geometry (2018)
  • Author(s): Mineyama Ryosuke、Oguni Shin-ichi
  • Journal Title: Monatshefte fur Mathematik Volume: 187 Issue: 4 Pages: 665-680
  • DOI: 10.1007/s00605-018-1171-1
  • Peer Reviewed
• [Presentation] Artin-Tits群の非シリンダー的双曲性について (2020)
  • Author(s): 尾國新一
  • Organizer: 一般位相幾何学とその関連分野の進展
• [Presentation] Artin群の非シリンダー的双曲性について (2020)
  • Author(s): 尾國新一
  • Organizer: 第15回代数・解析・幾何学セミナー
  • Invited
• [Presentation] On a coarse Cartan-Hadamard theorem (2019)
  • Author(s): Shin-ichi Oguni
  • Organizer: AMS Sectional meeting
  • Int'l Joint Research / Invited
• [Presentation] Coarsely convex spaces and a coarse Cartan-Hadamard theorem (2018)
  • Author(s): 尾國 新一
  • Organizer: トポロジー火曜セミナー
• [Presentation] On a coarse Cartan-Hadamard theorem (2018)
  • Author(s): Shin-ichi Oguni
  • Organizer: Rigidity School―The Final Meeting
• [Presentation] 粗凸距離空間入門 (2018)
  • Author(s): 尾國新一
  • Organizer: ワークショップ：幾何学的群論の新展開
• [Presentation] 粗幾何版アダマール・カルタンの定理について (2018)
  • Author(s): 尾國新一
  • Organizer: 日本数学会2018年度年会
• [Presentation] 粗ホモトピーについて (2017)
  • Author(s): 尾國新一
  • Organizer: 第3回幾何学的群論若手勉強会
  • Place of Presentation: ルネッサ赤沢（静岡県伊東市）
  • Year and Date: 2017-03-07
• [Presentation] On coarse homotopy (2017)
  • Author(s): 尾國新一
  • Organizer: 集合論的・幾何学的トポロジーの動向と諸分野との連携
• [Presentation] 粗幾何版アダマール・カルタンの定理とその応用 (2017)
  • Author(s): 尾國新一
  • Organizer: 松山TGSAセミナー
• [Remarks] 尾國新一(researchmap)
  • URL: https://researchmap.jp/oguni.shin-ichi
• [Remarks] 尾國新一(研究者要覧)
  • URL: https://yoran.office.ehime-u.ac.jp/Profiles/4/0000301/profile.html
• [Remarks] 尾國 新一（research map）
  • URL: https://researchmap.jp/7000014821/
• [Remarks] 尾國 新一（愛媛大学教育研究者要覧）
  • URL: http://yoran.office.ehime-u.ac.jp/profile/ja.5f17f12f60ba3cdd60392a0d922b9077.html