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 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
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.