Development of toric topology
Project/Area Number |
25400095
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
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) |
2013-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
|
Keywords | トーラス群 / 旗多様体 / コホモロジー / 特性類 / ルート系 / toric variety / 組合せ論 / Hessenberg variety / torus manifold / シンプレクティックトーリック多様体 / トーリック折り紙多様体 / コホモロジー環 / Peterson variety / コホモロジー剛性問題 / toric origami manifold |
Outline of Final Research Achievements |
I obtained the following results about the topology of manifolds with torus actions. ①We proved that any cohomology ring isomorphism between two Bott manifolds preserves their Pontrjagin classes (Joint work with Choi and Murai). ②We gave an explicit presentation of the cohomology ring strucure of Peterson varieties and regular nilpotent Hessenberg varieties which are subvarieties of flag varieties (joint work with Fukukawa-Harada, Harada-Horiguchi, Abe-Harada-Horiguchi). ③We studied the cohomology f toric origami manifolds (joint work with Ayzenberg, Park and Zeng). ④We studied the symmetry of torus manifolds by introducing a root system for a torus manifold (joint work with Kuroki).
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Report
(4 results)
Research Products
(31 results)