Conjugation spaces and equivariant Chern classes

Details Conjugation spaces and equivariant Chern classes Conjugation spaces and equivariant Chern classes

2011-12-19

arxiv.org/abs/1112.4357v2

Mathematics

Algebraic Topology

15 pages. This new version corrects the receptacle for the equivariant Chern classes of Real bundles by twisting the coefficie

Scientific paper

Let h be a Real bundle, in the sense of Atiyah, over a space X. This is a complex vector bundle together with an involution which is compatible with complex conjugation. We use the fact that BU is equipped with a structure of conjugation space, as defined by Hausmann, Holm, and Puppe, to construct equivariant Chern classes in the Z/2-equivariant cohomology of X with twisted integer coefficients. We show that these classes determine the (non-equivariant) Chern classes of h, forgetting the involution on X, and the Stiefel-Whitney classes of the real bundle of fixed points.

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