Characteristic classes on Grassmannians
Authors : Jin Shi, Jianwei Zhou
Pages : 492-523
Doi:10.3906/mat-1302-54
View : 7 | Download : 5
Publication Date : 9999-12-31
Article Type : Makaleler
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: Hq(G(k,n), R) \to Hk(n-k)-q(G(k,n), R) can be expressed explicitly.Keywords : Grassmann manifold, fibre bundle, characteristic class, homology group, Poincaré duality