Masteruppsatser

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Browsing Masteruppsatser by Author "Anghammar, Oscar"

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    Singular and de Rham cohomology for the Grassmannian
    (2015-09-16) Anghammar, Oscar; University of Gothenburg/Department of Mathematical Science; Göteborgs universitet/Institutionen för matematiska vetenskaper
    We compute the Poincar e polynomial for the complex Grassmannian using de Rham cohomology. We also construct a CW complex on the Grassmannian using Schubert cells, and then we use these cells to construct a basis for the singular cohomology. We give an algorithm for calculating the number of cells, and use this to compare the basis in singular cohomology with the Poincar e polynomial from de Rham cohomology. We also explore Schubert calculus and the connection between singular cohomology on the complex Grassmannian and the possible triples of eigenvalues to Hermitian matrices A+B = C, and give a brief discussion on if and how cohomologies can be used in the case of real skew-symmetric matrices.