Characteristic classes on Grassmannians

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.

Anahtar Kelimeler:

Grassmann manifold, fibre bundle, characteristic class, homology group, Poincaré duality

Characteristic classes on Grassmannians

Keywords:

Grassmann manifold, fibre bundle, characteristic class, homology group, Poincaré duality,

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