2009 Fiscal Year Final Research Report
An algebraic topological approach to Schubert calculus
| Project/Area Number |
20840041
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| Research Category |
Grant-in-Aid for Young Scientists (Start-up)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Fukuoka University |
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Principal Investigator |
KAJI Shizuo Fukuoka University, 理学部, 助教 (00509656)
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| Project Period (FY) |
2008 – 2009
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| Keywords | 位相幾何学 / ホモトピー論 / リー群 / 群作用をもつ空間 / の位相不変量 / 旗多様体 |
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| Research Abstract |
The symmetry of spaces transformed continuously is mathematically described through actions of Lie groups, which can be caught by invariants of the Lie groups and the spaces acted by them. In this research project, we investigate Schubert calculus, the study of the geometry of a certain class of spaces called flag varieties, which appear as the quotient of Lie groups. We took an algebraic topological approach to it and calculated some invariants of flag varieties explicitly.
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