Conjugation spaces and equivariant Cheen classes

Wolfgang Pitsch, Jér̂ome Scherer

Research output: Contribution to journalArticleResearchpeer-review

4 Citations (Scopus)

Abstract

Let η 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) Chem classes of η, forgetting the involution on X, and the Stiefel-Whitney classes of the real bundle of fixed points.
Original languageEnglish
Pages (from-to)77-90
JournalBulletin of the Belgian Mathematical Society - Simon Stevin
Volume20
Issue number1
Publication statusPublished - 1 Jan 2013

Keywords

  • Characteristic classes
  • Conjugation spaces
  • Equivariant chern classes

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