Relatively hyperbolic structures and convergence actions of discrete groups

• Project/Area Number: 24740045
• 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, 准教授 (00549446)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Project Status: Completed (Fiscal Year 2015)
• Budget Amount: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000); Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
• Keywords: 相対的双曲群 / 粗幾何 / 幾何学的群論 / 幾何学 / 粗幾何学

Outline of Final Research Achievements

My research mainly treated relatively hyperbolic groups and related topics. Actually some properties with respect to geometric group theory, dynamical system, coarse geometry, non-commutative geometry and so on were studied. In particular some new theorems related to boundaries of relatively hyperbolic groups were proved. Such results were presented in my talks in some conferences and in papers. For example joint works with Yoshifumi Matsuda and Saeko Yamagata are related to geometric group theory and dynamical system. Also joint works with Tomohiro Fukaya deal with coarse geometric and non-commutative geometric properties.

Research Products

• [Journal Article] The coarse Baum-Connes conjecture for Busemann non-positively curved spaces (2016)
  • Author(s): Tomohiro Fukaya, Shin-ichi Oguni
  • Journal Title: Kyoto Journal of Mathematics Volume: 56(1) Issue: 1 Pages: 1-12
  • DOI: 10.1215/21562261-3445129
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Notes on relatively hyperbolic groups and relatively quasiconvex subgroups (2015)
  • Author(s): Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
  • Journal Title: Tokyo Journal of Mathematics Volume: 38(1) Issue: 1 Pages: 99-123
  • DOI: 10.3836/tjm/1428412566
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Coronae of product spaces and the coarse Baum-Connes conjecture (2015)
  • Author(s): Tomohiro Fukaya, Shin-ichi Oguni
  • Journal Title: Advances in Mathematics Volume: 279 Pages: 201-233
  • DOI: 10.1016/j.aim.2015.01.022
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Coronae of relatively hyperbolic groups and coarse cohomologies (2015)
  • Author(s): Tomohiro Fukaya, Shin-ichi Oguni
  • Journal Title: Journal of Topology and Analysis Volume: online Issue: 03 Pages: 1-44
  • DOI: 10.1142/s1793525316500151
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] The universal relatively hyperbolic structure on a group and relative quasiconvexity for subgroups (2014)
  • Author(s): Y. Matsuda, S. Oguni, S. Yamagata
  • Journal Title: RIMS Kokyuroku Bessatsu B Volume: 48 Pages: 73-93
  • Peer Reviewed
• [Journal Article] On Cannon-Thurston maps for relatively hyperbolic groups (2014)
  • Author(s): Yoshifumi Matsuda; Shin-ichi Oguni
  • Journal Title: Journal of Group Theory Volume: 17(1) Issue: 1 Pages: 41-47
  • DOI: 10.1515/jgt-2013-0024
  • Peer Reviewed
• [Journal Article] C*-simplicity for groups with non-elementary convergence group actions (2013)
  • Author(s): Yoshifumi Matsuda, Shin-ichi Oguni, Saeko Yamagata
  • Journal Title: Houston Journal of Mathematics Volume: 39(4) Pages: 1291-1299
  • Peer Reviewed
• [Journal Article] Dilatational equivalence classes, Novikov-Shubin type capacities of groups, and random walks (2013)
  • Author(s): Shin-ichi Oguni
  • Journal Title: Noncommutative Geometry and Physics Volume: 3 Pages: 433-469
  • Peer Reviewed
• [Presentation] Coronae of product spaces and the coarse Baum-Connes conjecture (2015)
  • Author(s): Shin-ichi Oguni
  • Organizer: International Conference on Non-commutative Geometry and K-Theory
  • Place of Presentation: 重慶（中国）
  • Year and Date: 2015-12-18
  • Int'l Joint Research
• [Presentation] 粗Baum-Connes予想と粗幾何 (2015)
  • Author(s): 尾國新一
  • Organizer: 広島幾何学研究集会2015
  • Place of Presentation: 広島大学（広島県・東広島市）
  • Year and Date: 2015-10-07
• [Presentation] 粗Baum-Connes予想と粗代数的トポロジー (2014)
  • Author(s): 尾國新一
  • Organizer: 日本数学会2014年度秋季総合分科会
  • Place of Presentation: 広島大学（広島県東広島市）
  • Year and Date: 2014-09-25 – 2014-09-28
  • Invited
• [Presentation] Coarse Baum-Connes conjecture and coarse algebraic topology (2014)
  • Author(s): 尾國 新一
  • Organizer: Rigidity School, Tokyo 2013/2014
  • Place of Presentation: 東京大学
• [Presentation] Coronae and coarse homologies (2013)
  • Author(s): 尾國 新一
  • Organizer: Metric geometry and analysis
  • Place of Presentation: 京都大学
• [Presentation] On the coarse Baum-Connes conjecture (2013)
  • Author(s): 尾國 新一
  • Organizer: GEOQUANT 2013
  • Place of Presentation: ESI, Vienna, Austria
• [Presentation] The coarse Baum-Connes conjecture for relatively hyperbolic groups (2013)
  • Author(s): 尾國 新一
  • Organizer: China-Japan Conference on Noncommutative Geometry and K-Theory
  • Place of Presentation: Jilin University, Changchun, China
• [Presentation] The coarse Baum-Connes conjecture for relatively hyperbolic groups
  • Author(s): Shin-ichi Oguni
  • Organizer: Geometric group theory and K-theory
  • Place of Presentation: 鳥羽シーサイドホテル
• [Presentation] The coarse Baum-Connes conjecture for relatively hyperbolic groups
  • Author(s): 尾國新一
  • Organizer: 非可換幾何学と数理物理学２０１２
  • Place of Presentation: 慶應義塾大学
• [Remarks] 愛媛大学研究者総覧（尾國新一）
  • URL: http://kenqweb.office.ehime-u.ac.jp/Profiles/0010/0002335/profile.html
• [Remarks] 愛媛大学最先端研究紹介infinity（尾國新一）
  • URL: https://www.ehime-u.ac.jp/data_study/data_study-6025/