Study of embedding spaces using operads

• Project/Area Number: 26800037
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Osaka Prefecture University (2015-2017); Doshisha University (2014)
• Principal Investigator: Moriya Syunji 大阪府立大学, 理学(系)研究科(研究院), 客員研究員 (40583464)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Project Status: Completed (Fiscal Year 2017)
• Budget Amount: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000); Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
• Keywords: オペラッド / 高次ホモトピー / ホモトピー論 / 結び目 / 代数的位相幾何 / 形式性

Outline of Final Research Achievements

I studied the relationship between high codimensional long knots and operads.Operads control algebraic structures. I proved the odd dimensional framed little disks operads is not formal, which is not expected by many researchers.

Research Products

• [Journal Article] The space of short ropes and the classifying space of the space of long knots (2018)
  • Author(s): Syunji Moriya, Keiichi Sakai
  • Journal Title: Algebraic & Geometric Topology Volume: -
  • Peer Reviewed
• [Journal Article] Non-formality of the odd dimensional framed little disks operads (2017)
  • Author(s): Syunji Moriya
  • Journal Title: International Mathematics Research Notices Volume: - Issue: 2 Pages: 625-639
  • DOI: 10.1093/imrn/rnx144
  • Peer Reviewed
• [Presentation] Non-formality of the odd dimensional framed little disks operads (2018)
  • Author(s): 森谷 駿二
  • Organizer: 日本数学会2018年度年会
• [Presentation] The space of knots in manifolds and right A-infinity modules of configuration spaces (2018)
  • Author(s): 森谷 駿二
  • Organizer: 日本数学会2018年度年会
• [Presentation] The space of short ropes and the classifying space of the space of long knots (2017)
  • Author(s): 森谷駿二 境圭一
  • Organizer: 日本数学会2017年度年会
  • Place of Presentation: 首都大学東京
• [Presentation] The space of short ropes and the classifying space of the space of long knots (2017)
  • Author(s): 森谷 駿二
  • Organizer: Topology seminar
  • Place of Presentation: Kansas State University
  • Int'l Joint Research / Invited
• [Presentation] The space of short ropes and the classifying space of the space of long knots (2017)
  • Author(s): 森谷駿二 境圭一
  • Organizer: 福岡ホモトピー論セミナー
  • Place of Presentation: 福岡大学セミナーハウス
• [Presentation] On the rational homology of a space of knots in a manifold of dimension greater than 3 (2016)
  • Author(s): 森谷 駿二
  • Organizer: 信州トポロジーセミナー
  • Place of Presentation: 信州大学理学部 A 棟 4 階 数理攻究室(長野県松本市)
  • Year and Date: 2016-03-15
  • Invited
• [Presentation] Rational homotopy theory and knots in a manifold (2016)
  • Author(s): 森谷 駿二
  • Organizer: 福岡ホモトピー論セミナー
  • Place of Presentation: 福岡大学セミナーハウス（福岡県福岡市中央区）
  • Year and Date: 2016-01-11
• [Presentation] Non-formality of odd dimensional framed little disks operad (2014)
  • Author(s): 森谷駿二
  • Organizer: 信州トポロジーセミナー
  • Place of Presentation: 信州大学
  • Year and Date: 2014-12-10
• [Presentation] Non-formality of odd dimensional framed little disks operad (2014)
  • Author(s): 森谷駿二
  • Organizer: ホモトピー論シンポジウム
  • Place of Presentation: 大阪府立大学
  • Year and Date: 2014-11-03
• [Presentation] Non-formality of odd dimensional framed little disks operad (2014)
  • Author(s): 森谷駿二
  • Organizer: ICM satellite conference on algebraic topology
  • Place of Presentation: 中国 大連
  • Year and Date: 2014-08-10