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Transferred Chern classes in Morava $K$-theory


Authors: Malkhaz Bakuradze and Stewart Priddy
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 1855-1860
MSC (2000): Primary 55R12, 55R20; Secondary 55R40
DOI: https://doi.org/10.1090/S0002-9939-03-07265-4
Published electronically: December 18, 2003
Erratum: Proc. Amer. Math. Soc. (recently posted)
MathSciNet review: 2051151
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $\eta$ be a complex $n$-plane bundle over the total space of a cyclic covering of prime index $p$. We show that for $k\in \{1,2,...,np\} \setminus \{p,2p,...,np \}$ the $k$-th Chern class of the transferred bundle differs from a certain transferred class $\omega_k$ of $\eta$ by a polynomial in the Chern classes $c_p,...,c_{np}$ of the transferred bundle. The polynomials are defined by the formal group law and certain equalities in $K(s)^*B(Z/p \times U(n))$.


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Additional Information

Malkhaz Bakuradze
Affiliation: Razmadze Mathematical Institute, Tbilisi 380093, Republic of Georgia
Address at time of publication: Max-Planck-Institut Für Mathematik, Bonn, Germany
Email: bakuradz@mpim-bonn.mpg.de

Stewart Priddy
Affiliation: Department of Mathematics, Northwestern University, Evanston, Illinois 60208
Email: priddy@math.northwestern.edu

DOI: https://doi.org/10.1090/S0002-9939-03-07265-4
Keywords: Transfer, formal group law, Chern class
Received by editor(s): October 24, 2002
Received by editor(s) in revised form: February 24, 2003
Published electronically: December 18, 2003
Additional Notes: The first author was supported by the Max Planck Institute of Mathematics and CRDF grant GM1 2083
The second author was partially supported by the NSF
Communicated by: Paul Goerss
Article copyright: © Copyright 2003 American Mathematical Society

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