#### Volume 3, issue 1 (2003)

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Transfer and complex oriented cohomology rings

### Malkhaz Bakuradze and Stewart Priddy

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
##### Publication
Received: 26 September 2002
Revised: 12 May 2003
Accepted: 5 June 2003
Published: 5 June 2003
##### Authors
 Malkhaz Bakuradze Razmadze Mathematical Institute Tbilisi 380093 Republic of Georgia Stewart Priddy Department of Mathematics Northwestern University Evanston IL 60208 USA