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Morava K-theory of the exceptional Lie group and flag manifold

Research Project

Project/Area Number 24540102
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionKobe University of Welfare

Principal Investigator

NISHIMOTO Tetsu  神戸医療福祉大学, 社会福祉学部, 准教授 (80330520)

Co-Investigator(Renkei-kenkyūsha) MIMURA Mamoru  岡山大学, 名誉教授 (70026772)
NAKAGAWA Masaki  岡山大学, 教育学研究科, 准教授 (50370036)
Project Period (FY) 2012-04-01 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Keywordsトポロジー / リー群
Outline of Final Research Achievements

In order to know the property of the fibre bundle, there is a way to calculate the characteristic classes. The most important fibre bundle is the universal bundle, and to determine its characteristic classes is equivalent to calculate the cohomology of the classifying space of the structure group. The spectral sequence is the tool to calculate the cohomology of the classifying space. This time, I calulated the E_2-term of the spectral sequence convergence to the mod 3 cohomology of the classifying spaces of the exceptional Lie groups E_7 and E_8. Moreover, I calculated the invariant ring of the Weyl group of E_7 which acts on the mod 3 cohomology of the classifying space of the maximal torus.

Report

(4 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (1 results)

All 2014

All Presentation (1 results)

  • [Presentation] 数式処理システム Singular を使ったコホモロジーの計算2014

    • Author(s)
      西本哲
    • Organizer
      春の代数的位相幾何学セミナー
    • Place of Presentation
      岡山大学
    • Related Report
      2013 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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