Transfer and complex oriented cohomology rings

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 $T r^{*} (1)$ ) 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

Mathematical Subject Classification 2000

Primary: 55N22

Secondary: 55R12

References

Forward citations

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

Volume 3, issue 1 (2003)

Malkhaz Bakuradze and Stewart Priddy