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

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540102
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kobe 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
• 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.

Free Research Field

代数的位相幾何学