Annihilation in spectral sequences and cohomology of classifying spaces
| Project/Area Number |
25400097
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Shibaura Institute of Technology |
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Principal Investigator |
Kameko Masaki 芝浦工業大学, システム理工学部, 教授 (50270343)
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| Co-Investigator(Renkei-kenkyūsha) |
YAGITA Nobuaki 茨城大学, 教育学部, 名誉教授 (20130768)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 分類空間 / コホモロジー / スペクトル系列 / ループ空間 / チャウ環 / サイクル写像 / 有限シュバレー群 / トポロジー / スチーンロッド代数 / モチービックコホモロジー / ホッジ予想 / テイト予想 / 代数幾何 / 特性類 |
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| Outline of Final Research Achievements |
For a group G, there exists a space BG called the classifying space. The classifying space is a topological space and so one may study the group cohomology using tools in algebraic topology. Among tools available in algebraic topology are various spectral sequences. In our research project, we attempted to compute the cohomology of the classifying space BG using spectral sequences. In most successful cases, the spectral sequence collapses at the E_2 level. However, for some groups, the spectral sequence does not collapse at the E_2-level. In this research project, we dealt with such cases.
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Report
(6 results)
Research Products
(18 results)
