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

 

Operations and Spectral Sequences. I


Author: James M. Turner
Journal: Trans. Amer. Math. Soc. 350 (1998), 3815-3835
MSC (1991): Primary 18G40, 55S05, 55U15; Secondary 18G30, 55S10, 55S12, 55T10, 55T20
MathSciNet review: 1487634
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Abstract: Using methods developed by W. Singer and J. P. May, we describe a systematic approach to showing that many spectral sequences, determined by a filtration on a complex whose homology has an action of operations, possess a compatible action of the same operations. As a consequence, we obtain W. Singer's result for Steenrod operations on Serre spectral sequence and extend A. Bahri's action of Dyer-Lashof operations on the second quadrant Eilenberg-Moore spectral sequence.


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Additional Information

James M. Turner
Affiliation: Department of Mathematics, College of The Holy Cross, One College Street, Worcester, Massachusetts 01610-2395
Address at time of publication: Department of Mathematics, Calvin College, 3201 Burton Street, S.E., Grand Rapids, Michigan 49546-4388
Email: jmt@ziplink.net

DOI: http://dx.doi.org/10.1090/S0002-9947-98-02254-5
PII: S 0002-9947(98)02254-5
Keywords: Spectral sequences, Dold algebras, Steenrod operations, Dyer-Lashof operations, cosimplicial spaces, infinite loop spaces
Received by editor(s): October 21, 1996
Article copyright: © Copyright 1998 American Mathematical Society