2015 Fiscal Year Final Research Report
Development of toric topology
Project/Area Number |
25400095
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Research Category |
Grant-in-Aid for Scientific Research (C)
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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
|
Keywords | トーラス群 / 旗多様体 / コホモロジー / 特性類 / ルート系 |
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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Free Research Field |
トポロジー
|