Pitsch, Wolfgang
Scherer, Jerome
Conjugation spaces and equivariant Chern classes
Bulletin Of The Belgian Mathematical Society-Simon Stevin
1370-1444
20
1
77-90
14
Let eta 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 has a canonical structure of a conjugation space, as defined by Hausmann, Holm, and Puppe, to construct equivariant Chem classes in certain equivariant cohomology groups of X with twisted integer coefficients. We show that these classes determine the (non-equivariant) Chern classes of eta, forgetting the involution on X, and the Stiefel-Whitney classes of the real bundle of fixed points.
Conjugation spaces;
characteristic classes;
equivariant Chem classes;
Belgian Mathematical Soc Triomphe
Brussels
2013