An algebraic topological approach to Schubert calculus

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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.