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

Vimala Ramani

International Journal of Scientific Research in Science and Technology, 2024, vol. 11, issue 6, 680-685

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) .

Keywords: Complex Grassmann manifold; Chern classes; height; complex flag manifold (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
https://ijsrst.com/home/article/view/IJSRST241161123 Abstract page (text/html)
https://ijsrst.com/home/article/download/IJSRST241161123/IJSRST241161123 Full text (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:etm:ijsrst:v11:y2024:i6:id:497

DOI: 10.32628/IJSRST241161123

Access Statistics for this article

More articles in International Journal of Scientific Research in Science and Technology from Technoscience Academy
Bibliographic data for series maintained by Pankaj Sharma ().