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An Algebraic Computation of the Height of the First Chern Class of the Canonical K-Plane Bundle over the Complex Grassmannian CG_(n,k)

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  • Vimala Ramani

Abstract

We prove algebraically that the height of the first Chern class of the canonical k-plane bundle over the complex Grassmannian CG_(n,k) is k(n-k) in H^* ( CG_(n,k);Q) for k=2,3,4, and any positive integer n≥2k. We use the technique of R. E. Stong, of embedding the rational cohomology ring of the complex Grassmannian CG_(n,k) into the rational cohomology ring of the complete complex flag manifold F_C (⏟(1,…,1)┬n) .

Suggested Citation

  • Vimala Ramani, 2024. "An Algebraic Computation of the Height of the First Chern Class of the Canonical K-Plane Bundle over the Complex Grassmannian CG_(n,k)," International Journal of Scientific Research in Science and Technology, Technoscience Academy, vol. 11(6), pages 680-685, December.
    • Handle: RePEc:etm:ijsrst:v11:y2024:i6:id:497
    DOI: 10.32628/IJSRST241161123
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