Characteristic classes on Grassmannians | Zendy

Jin Shi | Zendy; Jianwei Zhou | Zendy

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Characteristic classes on Grassmannians

Author(s) -

Jin Shi,

Jianwei Zhou

Publication year - 2014

Publication title -

turkish journal of mathematics

Language(s) - English

Resource type - Journals

eISSN - 1303-6149

pISSN - 1300-0098

DOI - 10.3906/mat-1302-54

Subject(s) - mathematics , poincaré duality , characteristic class , cohomology , euler characteristic , homology (biology) , duality (order theory) , pure mathematics , vector bundle , grassmannian , exterior algebra , combinatorics , topology (electrical circuits) , algebra over a field , chemistry , gene , biochemistry

In this paper, we study the geometry and topology on the oriented Grassmann manifolds. In particular, we use characteristic classes and the Poincare 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 Poincare duality: Hq(G(k,n), R) \to Hk(n-k)-q(G(k,n), R) can be expressed explicitly.

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