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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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 Tr(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
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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