On the unstable higher order periodicity in model categories

• Project/Area Number: 17540070
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Shinshu University
• Principal Investigator: TAMAKI Dai Shinshu University, 理学部, 准教授 (10252058)
• Project Period (FY): 2005 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,600,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥300,000); Fiscal Year 2008: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2007: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000); Fiscal Year 2006: ¥800,000 (Direct Cost: ¥800,000); Fiscal Year 2005: ¥1,500,000 (Direct Cost: ¥1,500,000)
• Keywords: 多重ループ空間 / 超平面配置 / Salvetti複体 / K理論 / twisted K理論 / 両側bar構成 / twisted K / バー構成 / Kホモロジー / 超平面配置の補集合の空間 / 2重ループ空間 / 有向マトロイド / 局所係数ホモロジー / オペラッド / Eilenberg-Mooreスペクトル系列 / 配位空間 / operad / Salvetti complex / cobar construction / matroid / arrangement

Research Abstract

本研究の主な成果は大きく分けて次の二つである。一つは多重ループ空間のホモロジー群を計算するための主要なスペクトル系列の一つであるEilenberg-Mooreスペクトル系列の全く異なるアプローチによる構成を発見し, それによりEilenberg-Mooreスペクトル系列を一般化する新しいスペクトル系列の構成に成功したことである。もう一つは, 数理物理学への応用から発見されたK理論の変種であるtwisted K理論について, その連結ホモロジー版を新しい視点から構成することに成功したことである。

Research Products

• [Journal Article] Two-sided bar constructions for partial monoids and applications to K-homology theory (2009)
  • Author(s): Dai Tamaki
  • Journal Title: Noncommutative Geometry and Physics vol.3(印刷中)
  • Peer Reviewed
• [Journal Article] Twisting Segal's K-homology theory (2009)
  • Author(s): Dai Tamaki
  • Journal Title: Noncommutative Geometry and Physics vol.3(印刷中)
  • Peer Reviewed
• [Journal Article] Two-sided Bar Cons tructions for Partial Monoids and Applications to K-Homology Theory (2009)
  • Author(s): Dai Tamaki
  • Journal Title: Noncommutative Geometry and Physics 3(印刷中)
  • Peer Reviewed
• [Journal Article] Twisting Segal's K-Homology Theory (2009)
  • Author(s): Dai Tamaki
  • Journal Title: Noncommutative Geometry and Physics 3(印刷中)
  • Peer Reviewed
• [Journal Article] On the E^1-term of the gravity spectral sequence (2007)
  • Author(s): Dai Tamaki
  • Journal Title: Geometry and Topology Monographs vol.10 Pages: 341-376
  • Peer Reviewed
• [Journal Article] On the E^1-term of the gravity spectral sequence (2006)
  • Author(s): Dai Tamaki
  • Journal Title: Geometry and Topology Monograph 10 Pages: 341-376
• [Journal Article] On the E^1-term of the gravity spectral sequence (2006)
  • Author(s): Dai Tamaki
  • Journal Title: Geometry and Topology-Monographs (印刷中)
• [Presentation] On classifying spaces of partially defined algebraic structures (2009)
  • Author(s): Dai Tamaki
  • Organizer: 代数・解析・幾何学セミナー
  • Place of Presentation: 鹿児島大学
  • Year and Date: 2009-02-19
• [Presentation] On Classifying Spaces of Partially Defined Algebraic Structures (2009)
  • Author(s): Dai Tamaki
  • Organizer: 代数・解析・幾何学セミナー
  • Place of Presentation: 鹿児島大学
  • Year and Date: 2009-02-19
• [Presentation] Twisting Segal's K-homology theory (2008)
  • Author(s): Dai Tamaki
  • Organizer: 東アジア代数的トポロジー国際会議
  • Place of Presentation: シンガポール国立大学
  • Year and Date: 2008-12-19
• [Presentation] Twisting Sega's K-Homology Theory (2008)
  • Author(s): Dai Tamaki
  • Organizer: 東アジア代数的トポロジー国際会議
  • Place of Presentation: シンガポール国立大学
  • Year and Date: 2008-12-19
• [Presentation] Twisting Segal's K-homology theory (2008)
  • Author(s): Dai Tamaki
  • Organizer: ホモトピー論研究集会
  • Place of Presentation: サンポート高松
  • Year and Date: 2008-12-06
• [Presentation] Twisting Segal's K-Homology Theory (2008)
  • Author(s): Dai Tamaki
  • Organizer: ホモトピー論研究集会
  • Place of Presentation: サンポート高松
  • Year and Date: 2008-12-06
• [Presentation] Hyperplane arrangements for iterated loop spaces (2008)
  • Author(s): Dai Tamaki
  • Organizer: 超平面配置のさまざまな側面
  • Place of Presentation: 神戸大学
  • Year and Date: 2008-02-05
• [Presentation] Hyperpiane arrangements for iterated loop spaces (2008)
  • Author(s): 玉木 大
  • Organizer: 超平面配置のさまざまな側面
  • Place of Presentation: 神戸大学
  • Year and Date: 2008-02-05
• [Presentation] A homotopical introduction to twisted K-theory (2008)
  • Author(s): Dai Tamaki
  • Organizer: Noncommutative Geometry and Physics 2008
  • Place of Presentation: 湘南国際村
• [Presentation] A homotopical introductioin to twisted K-theory (2008)
  • Author(s): Dai Tamaki
  • Organizer: Noncommutative Geometry and Physics 2008
  • Place of Presentation: 湘南国際村
• [Presentation] Iterated loop spaces and oriented matroids (2007)
  • Author(s): Dai Tamaki
  • Organizer: International Conference on Topology and its Applications
  • Place of Presentation: 京都大学
  • Year and Date: 2007-12-05
• [Presentation] Iterated loop spaces and oriented matroids (2007)
  • Author(s): Dai Tamaki
  • Organizer: International Conference on Topology and its Applications 2007
  • Place of Presentation: 京都大学
  • Year and Date: 2007-12-05
• [Presentation] The little cubes and the Salvetti complex (2007)
  • Author(s): Dai Tamaki
  • Organizer: 東アジア代数的トポロジー国際会議
  • Place of Presentation: ソウル国立大学
  • Year and Date: 2007-11-03
• [Presentation] The little cubes and the Salvetti complex (2007)
  • Author(s): Dai Tamaki
  • Organizer: East Asian Conference on Algebraic Topology
  • Place of Presentation: ソウル大学
  • Year and Date: 2007-11-03
• [Presentation] 組み合せ論とホモトピー論はより親密になれるか (2007)
  • Author(s): Dai Tamaki
  • Organizer: NYメイツの集い-名工大ホモトピー論集会07-
  • Place of Presentation: 名古屋工業大学
  • Year and Date: 2007-03-24
• [Presentation] Oriented n-matroids and little n-cubes (2006)
  • Author(s): Dai Tamaki
  • Organizer: 空間の代数的・幾何学的モデルとその周辺
  • Place of Presentation: 信州大学
  • Year and Date: 2006-09-06
• [Presentation] Homology theory and categorification (2005)
  • Author(s): Dai Tamaki
  • Organizer: 城崎新人セミナー
  • Place of Presentation: 城崎健康福祉センター
  • Year and Date: 2005-02-23
• [Book] 一般コホモロジー (2008)
  • Author(s): 河野明, 玉木大
  • Total Pages: 258
  • Publisher: 岩波書店
• [Book] Generalized Cohomology (2006)
  • Author(s): Akira Kono and Dai Tamaki
  • Total Pages: 264
  • Publisher: the American Mathematical Society
• [Book] Generalized Cohomology (2006)
  • Author(s): Akira kono, Dai Tamaki
  • Total Pages: 264
  • Publisher: The American Mathematical Society
• [Book] Generalized Cohomology (2006)
  • Author(s): Akira Kono, Dai Tamaki
  • Total Pages: 264
  • Publisher: The American Mathematical Society
• [Remarks]
  • URL: http://pantodon.shinshu-u.ac.ip/topoloav/literature/
• [Remarks]
  • URL: http://pantodon.shinshu-u.ac.jp/topology/literature/