Turkish Journal of Mathematics
DOI
10.3906/mat-1302-54
Abstract
In this paper, we study the geometry and topology on the oriented Grassmann manifolds. In particular, we use characteristic classes and the Poincaré duality to study the homology groups of Grassmann manifolds. We show that for k=2 or n \leq 8, the cohomology groups H^*(G(k,n), R) are generated by the first Pontrjagin class, the Euler classes of the canonical vector bundles. In these cases, the Poincaré duality: H^q(G(k,n), R) \to H_{k(n-k)-q}(G(k,n), R) can be expressed explicitly.
Keywords
Grassmann manifold, fibre bundle, characteristic class, homology group, Poincaré duality
First Page
492
Last Page
523
Recommended Citation
SHI, JIN and ZHOU, JIANWEI
(2014)
"Characteristic classes on Grassmannians,"
Turkish Journal of Mathematics: Vol. 38:
No.
3, Article 12.
https://doi.org/10.3906/mat-1302-54
Available at:
https://journals.tubitak.gov.tr/math/vol38/iss3/12
