Algebraic & Geometric Topology

Transfer and complex oriented cohomology rings

Malkhaz Bakuradze and Stewart Priddy

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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.

Article information

Source
Algebr. Geom. Topol., Volume 3, Number 1 (2003), 473-509.

Dates
Received: 26 September 2002
Revised: 12 May 2003
Accepted: 5 June 2003
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882380

Digital Object Identifier
doi:10.2140/agt.2003.3.473

Mathematical Reviews number (MathSciNet)
MR1997326

Zentralblatt MATH identifier
1026.55020

Subjects
Primary: 55N22: Bordism and cobordism theories, formal group laws [See also 14L05, 19L41, 57R75, 57R77, 57R85, 57R90]
Secondary: 55R12: Transfer

Keywords
transfer Chern class classifying space complex cobordism Morava K–theory

Citation

Bakuradze, Malkhaz; Priddy, Stewart. Transfer and complex oriented cohomology rings. Algebr. Geom. Topol. 3 (2003), no. 1, 473--509. doi:10.2140/agt.2003.3.473. https://projecteuclid.org/euclid.agt/1513882380


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