Development of toric topology

• Project/Area Number: 22540094
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Geometry
• Research Institution: Osaka City University
• Principal Investigator: MASUDA Mikiya 大阪市立大学, 大学院・理学研究科, 教授 (00143371)
• Project Period (FY): 2010 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000); Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2011: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000); Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 位相幾何 / トーリック幾何 / トーラス多様体 / 多重扇 / シンプレクティック幾何 / small cover / 格子点 / GKMグラフ / トポロジー / トーリック多様体 / 組合せ論 / 群 / ルート系

Research Abstract

With Ishida and Fukukawa, I introduced the notions of a topological toric manifold (a topological generalization of a toric manifold) and a topological fan (a generalization of fan) and showed that there is a bijective correspondence between those objects

Research Products

• [Journal Article] Topological toric manifolds (2013)
  • Author(s): H. Ishida and Y. Fukukawa, M. Masuda
  • Journal Title: Moscow Math. J Volume: 13, no. 1 Pages: 57-98
  • Peer Reviewed
• [Journal Article] Topological toric manifolds (2013)
  • Author(s): Hiroaki Ishida
  • Journal Title: Moscow Mathematical Journal Volume: 13 Pages: 57-98
  • Peer Reviewed
• [Journal Article] TODD GENERA OF COMPLEX TORUS MANIFOLDS (2012)
  • Author(s): H. Ishida and M. Masuda
  • Journal Title: Algebraic & Geometric Topology Volume: 11 Issue: 20 Pages: 1-12
  • DOI: 10.2140/agt.2012.12.1777
  • URL: https://ocu-omu.repo.nii.ac.jp/records/2016772
  • Peer Reviewed
• [Journal Article] Classification of Q-trivial Bott manifolds (2012)
  • Author(s): S. Choi and M. Masuda
  • Journal Title: J. Symplectic Geom Volume: 10, no. 3 Pages: 447-461
  • Peer Reviewed
• [Journal Article] Buchstaber invariants of skeleta of a simplex. (2011)
  • Author(s): Y. Fukukawa, M. Masuda
  • Journal Title: Osaka J. Math. Volume: 48 Pages: 549-582
  • NAID: 120005986559
  • Peer Reviewed
• [Journal Article] Rigidity problems in toric topology, a survey (2011)
  • Author(s): S. Choi, M. Masuda and D. Y. Suh
  • Journal Title: Proc. of the Steklov Institute of Math Volume: Vol. 275 Pages: 177-190
  • Peer Reviewed
• [Journal Article] Buchstaber invariants of skeleta of a simplex (2011)
  • Author(s): Y.Fukukawa, M.Masuda
  • Journal Title: Osaka Journal of Mathematics Volume: 48 Pages: 549-582
  • NAID: 120005986559
  • Peer Reviewed
• [Journal Article] Rigidity problems in toric topology, a survey (2011)
  • Author(s): S.Choi, M.Masuda, D.Y.Suh
  • Journal Title: Proc.of the Steklov Institute of Math. Volume: 275 Pages: 177-190
  • Peer Reviewed
• [Journal Article] Topological classification of generalized Bott towers (2010)
  • Author(s): S. Choi, M. Masuda and D. Y. Suh
  • Journal Title: Trans. AMS Volume: 362 Pages: 1097-1112
  • Peer Reviewed
• [Journal Article] Quasitoric manifolds over a product of simplices (2010)
  • Author(s): S. Choi, M. Masuda and D. Y. Suh
  • Journal Title: Osaka J. Math Volume: vol. 47 Pages: 109-129
  • NAID: 120004841207
  • Peer Reviewed
• [Journal Article] Cohomological non-rigidity of generalized real Bott manifolds of height 2 (2010)
  • Author(s): M. Masuda
  • Journal Title: Proceedings of the Steklov Institute of Mathematics Volume: Vol. 268 Pages: 242-247
  • Peer Reviewed
• [Journal Article] Symmetry of a symplectic toric manifold (2010)
  • Author(s): M. Masuda
  • Journal Title: J. Symp. Geom. Volume: 8 Pages: 359-380
  • Peer Reviewed
• [Journal Article] トーリックトポロジー (2010)
  • Author(s): 枡田幹也
  • Journal Title: 数学 Volume: 62巻 Pages: 386-411
  • NAID: 10029848985
  • Peer Reviewed
• [Journal Article] Topological classification of generalized Bott towers (2010)
  • Author(s): S.Choi, M.Masuda, D.Y.Suh
  • Journal Title: Transactions of Amer.Math.Soc. Volume: 362 Pages: 1097-1112
  • Peer Reviewed
• [Journal Article] Quasitoric manifolds over a product of simplices (2010)
  • Author(s): S.Choi, M.Masuda, D.Y.Suh
  • Journal Title: Osaka Journal of Math. Volume: 47 Pages: 109-129
  • NAID: 120004841207
  • Peer Reviewed
• [Journal Article] Symmetry of a symplectic toric manifold (2010)
  • Author(s): M.Masuda
  • Journal Title: Journal of Symplectic Geometry Volume: 8 Pages: 359-380
  • Peer Reviewed
• [Journal Article] Cohomological non-rigidity of generalized real Bott manifolds of height 2 (2010)
  • Author(s): M.Masuda
  • Journal Title: Proc.of the Steklov Institute of Mathematics Volume: 268 Pages: 242-247
  • Peer Reviewed
• [Journal Article] Topology of iterated $S^1$-bundles
  • Author(s): J.B. Lee and M. Masuda
  • Journal Title: Osaka J. Math. Volume: (accepted)
  • NAID: 120005986438
  • Peer Reviewed
• [Presentation] Topological toric manifolds (2012)
  • Author(s): M. Masuda
  • Organizer: Toric Geometry
  • Place of Presentation: Oberwolfach ドイツ
  • Year and Date: 2012-04-20
• [Presentation] Some combinatorics and geometry in toric topology (2011)
  • Author(s): M. Masuda
  • Organizer: International Conference Toric Topology and Automorphic Functions
  • Place of Presentation: ハバロフスク,ロシア
  • Year and Date: 2011-09-05
• [Presentation] Some combinatorics and geometry in toric topology (2011)
  • Author(s): Mikiya Masuda
  • Organizer: International Conference Toric Topology and Automorphic Functions
  • Place of Presentation: ハバロフスク(ロシア)(招待講演)
  • Year and Date: 2011-09-05
• [Presentation] Iterated circle bundles (2011)
  • Author(s): M. Masuda
  • Organizer: 第3回国際ワークショップ 「微分幾何学と幾何解析」
  • Place of Presentation: 大阪市
  • Year and Date: 2011-03-13
• [Presentation] Iterated circle bundles (2011)
  • Author(s): M.Masuda
  • Organizer: 第3回国際ワークショップ「微分幾何学と幾何解析」
  • Place of Presentation: 大阪市立大学(招待講演)
  • Year and Date: 2011-03-13
• [Presentation] Iterated circle bundles (2011)
  • Author(s): M. Masuda
  • Organizer: アメリカ数学会
  • Place of Presentation: ハワイ大学(アメリカ)
  • Year and Date: 2011-03-03
• [Presentation] Iterated circle bundles (2011)
  • Author(s): Mikiya Masuda
  • Organizer: アメリカ数学会
  • Place of Presentation: ハワイ大学(招待講演)
  • Year and Date: 2011-03-03
• [Presentation] 私が遭遇したKervaire不変量 (2011)
  • Author(s): 枡田幹也
  • Organizer: 北田さんを囲む会
  • Place of Presentation: キャンパスプラザ京都(招待講演)
  • Year and Date: 2011-02-11
• [Presentation] Cohomological rigidity problem, topological toric manifolds and face numbers of simplicial cell manifolds (2010)
  • Author(s): M. Masuda
  • Organizer: Topological methods in toric geometry, symplectic geometry and combinatorics
  • Place of Presentation: Banff (カナダ)
  • Year and Date: 2010-11-09
• [Presentation] Cohomological rigidity problem, topological toric manifolds and face numbers of simplicial cell manifolds (2010)
  • Author(s): M.Masuda
  • Organizer: Topological methods in toric geometry, symplectic geometry and combinatorics
  • Place of Presentation: Banff(カナダ)(招待講演)
  • Year and Date: 2010-11-09
• [Presentation] Classification of real Bott manifolds and acyclic digraphs (2010)
  • Author(s): 枡田幹也
  • Organizer: 日本数学会トポロジー分科会
  • Place of Presentation: 名古屋大学(一般講演)
  • Year and Date: 2010-09-23
• [Presentation] シンプレクティックトーリック多様体のルート系 (2010)
  • Author(s): 枡田幹也
  • Organizer: 日本数学会トポロジー分科会
  • Place of Presentation: 名古屋大学(一般講演)
  • Year and Date: 2010-09-23
• [Presentation] Classification of real Bott manifolds and acyclic digraphs (2010)
  • Author(s): M. Masuda
  • Organizer: Workshop on Geometry & Topology 2010
  • Place of Presentation: Fribourg (スイス)
  • Year and Date: 2010-09-18
• [Presentation] Classification of real Bott manifolds and acyclic digraphs (2010)
  • Author(s): M.Masuda
  • Organizer: Workshop on Geometry & Topology 2010
  • Place of Presentation: Fribourg(スイス)(招待講演)
  • Year and Date: 2010-09-18
• [Presentation] Classification of real Bott manifolds and acyclic digraphs (2010)
  • Author(s): M. Masuda
  • Organizer: Group Actions in Topology and Analysis -4th GAF Conference
  • Place of Presentation: Milan(イタリア)
  • Year and Date: 2010-09-16
• [Presentation] Classification of real Bott manifolds and acyclic digraphs (2010)
  • Author(s): M.Masuda
  • Organizer: Group Actions in Topology and Analysis-4th GAF Conference
  • Place of Presentation: Milan 2010,(イタリア)(招待講演)
  • Year and Date: 2010-09-16
• [Presentation] Cohomological rigidity problems in toric topology (2010)
  • Author(s): M. Masuda
  • Organizer: The International Conference "GEOMETRY, TOPOLOGY,ALGEBRA and NUMBER THEORY, APPLICATIONS" dedicated to the 120th anniversary of Boris Delone
  • Place of Presentation: ロシア
  • Year and Date: 2010-08-18
• [Presentation] Cohomological rigidity problems in toric topology (2010)
  • Author(s): M.Masuda
  • Organizer: Delone 生誕120年国際会議
  • Place of Presentation: Steklov研究所(モスクワ)(招待講演)
  • Year and Date: 2010-08-18
• [Presentation] Cohomological rigidity problems in toric topology (2010)
  • Author(s): M.Masuda
  • Organizer: Chinese Academy colloquium
  • Place of Presentation: Chinese Academy of Science(中国)(招待講演)
  • Year and Date: 2010-07-01
• [Presentation] The root system of a symplectic toric manifold (2010)
  • Author(s): M. Masuda
  • Organizer: International Conference on Algebraic and Geometric Topology
  • Place of Presentation: Beijin (中国)
  • Year and Date: 2010-06-30
• [Presentation] The root system of a symplectic toric manifold (2010)
  • Author(s): M.Masuda
  • Organizer: International Conference on Algebraic and Geometric Topology
  • Place of Presentation: Beijing(中国)(招待講演)
  • Year and Date: 2010-06-30
• [Presentation] The root system of a torus manifold (2010)
  • Author(s): M. Masuda
  • Organizer: Workshop on ToricTopology and Related Topics
  • Place of Presentation: Fudan Univ. (中国)
  • Year and Date: 2010-05-02
• [Presentation] The root system of a torus manifold (2010)
  • Author(s): M.Masuda
  • Organizer: Workshop on Toric Topology and Related Topics
  • Place of Presentation: Fudan Univ.(中国)(招待講演)
  • Year and Date: 2010-05-02
• [Presentation] Topological toric manifolds
  • Author(s): Mikiya Masuda
  • Organizer: Toric Geometry
  • Place of Presentation: Oberwolfach（ドイツ）
  • Invited
• [Presentation] Toric origami 4-manifolds
  • Author(s): Mikiya Masuda
  • Organizer: Structures and Symmetries on Manifolds
  • Place of Presentation: 沖縄県青年会館
  • Invited