Algebraic and Geometric Topology 3 (2003), paper no. 15, pages 473-509.

Transfer and complex oriented cohomology rings

Malkhaz Bakuradze, Stewart Priddy

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 (i.e. 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

AMS subject classification. Primary: 55N22. Secondary: 55R12.

DOI: 10.2140/agt.2003.3.473

E-print: arXiv:math.AT/0307182

Submitted: 26 September 2002. (Revised: 12 May 2003.) Accepted: 5 June 2003. Published: 5 June 2003.

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Malkhaz Bakuradze, Stewart Priddy

Razmadze Mathematical Institute, Tbilisi 380093, Republic of Georgia
and
Department of Mathematics, Northwestern University, Evanston, IL 60208, USA

Email: maxo@rmi.acnet.ge, priddy@math.northwestern.edu

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