Local coefficients and Euler class groups

JOURNAL OF ALGEBRA

卷:322

Article

Mandal, Satya¹  Sheu, Albert J. L.¹ 

[1] Univ Kansas, Dept Math, Lawrence, KS 66045 USA

关键词: Projective modules;    Vector bundles;    Euler classes;   

DOI  :  10.1016/j.jalgebra.2009.09.012

来源: Elsevier

【 摘 要 】

In this paper, we establish an isomorphism between the Euler class group E(R(X), L) for a real smooth affine variety X = Spec(A) and the 0-th homology group H(0)(M(c); G) with local coefficients in a bundle G of groups constructed from the line bundle G over M corresponding to the orientation rank-1 projective module L, where M(c) is the compact part of the manifold M of real points in X. Then by Steenrod's Poincare duality between homology and cohomology groups with local coefficients, this isomorphism is identified with the Whitney class homomorphism. (C) 2009 Elsevier Inc. All rights reserved.

【 授权许可】

Free