Conjugation spaces and equivariant Chern classes
Abstract
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.
Keywords
Cite
@article{arxiv.1112.4357,
title = {Conjugation spaces and equivariant Chern classes},
author = {W. Pitsch and J. Scherer},
journal= {arXiv preprint arXiv:1112.4357},
year = {2012}
}
Comments
15 pages. This new version corrects the receptacle for the equivariant Chern classes of Real bundles by twisting the coefficients. When n is odd, we use the sign representation of C_2 on the integers, when n is even the action is trivial