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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Transfer and the spectral sequence of a fibration


Author: Carlos Prieto
Journal: Trans. Amer. Math. Soc. 271 (1982), 133-142
MSC: Primary 55R12; Secondary 55R20
MathSciNet review: 648082
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Abstract: The purpose of this paper is to show that transfers for fibrations behave well with respect to spectral sequences which are induced by filtrations of the base space. In particular, for the spectral sequence of a fibration (induced by the skeletal filtration of the base space), one obtains the expected effect on the $ {E_2}$-terms: We prove that the transfer in the $ {E_2}$-terms is determined by the transfer of the fiber (considered trivially as a fibration over a point). As an application, results of Atiyah on the $ K$-theory of classifying spaces are transcribed to generalized cohomology theories.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1982-0648082-X
PII: S 0002-9947(1982)0648082-X
Keywords: Transfer, spectral sequence of a filtration, spectral sequence of a fibration, Atiyah-Hirzebruch-Whitehead spectral sequence, Leray-Serre spectral sequence
Article copyright: © Copyright 1982 American Mathematical Society