Volume 3, issue 1 (2003)

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Transfer and complex oriented cohomology rings

Algebraic & Geometric Topology 3 (2003) 473–509
 arXiv: math.AT/0307182
Abstract

For finite coverings we elucidate the interaction between transferred Chern classes and Chern classes of transferred bundles. This involves computing the ring structure for the complex oriented cohomology of various homotopy orbit spaces. In turn these results provide universal examples for computing the stable Euler classes (ie $T{r}^{\ast }\left(1\right)$) and transferred Chern classes for $p$–fold covers. Applications to the classifying spaces of $p$–groups are given.

Keywords
transfer, Chern class, classifying space, complex cobordism, Morava K–theory
Primary: 55N22
Secondary: 55R12