Bulletin of the Belgian Mathematical Society - Simon Stevin

Conjugation spaces and equivariant Chern classes

Wolfgang Pitsch and Jérôme Scherer

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Abstract

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 Chern 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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin Volume 20, Number 1 (2013), 77-90.

Dates
First available in Project Euclid: 18 April 2013

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1366306715

Mathematical Reviews number (MathSciNet)
MR3082744

Zentralblatt MATH identifier
1278.57034

Subjects
Primary: 57R20: Characteristic classes and numbers 55N91: Equivariant homology and cohomology [See also 19L47]
Secondary: 55N15: $K$-theory [See also 19Lxx] {For algebraic $K$-theory, see 18F25, 19- XX} 55P92: Relations between equivariant and nonequivariant homotopy theory 55R10: Fiber bundles

Keywords
Conjugation spaces characteristic classes equivariant Chern classes

Citation

Pitsch, Wolfgang; Scherer, Jérôme. Conjugation spaces and equivariant Chern classes. Bull. Belg. Math. Soc. Simon Stevin 20 (2013), no. 1, 77--90.https://projecteuclid.org/euclid.bbms/1366306715


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