|
Operations and Spectral Sequences. I
Author(s):
James
M.
Turner
Journal:
Trans. Amer. Math. Soc.
350
(1998),
3815-3835.
MSC (1991):
Primary 18G40, 55S05, 55U15;
Secondary 18G30, 55S10, 55S12, 55T10, 55T20
Retrieve article in:
PDF
This article is available free of charge
Abstract |
References |
Similar articles |
Additional information
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.
References:
- 1.
- A. Bahri, Operations in the second quadrant Eilenberg-Moore spectral sequence J. Pure and Appl. Alg. 27(1983), 207-222 MR 85b:55031
- 2.
- A. K. Bousfield, On the homology spectral sequence of a cosimplicial space, Amer. J. of Math. 109(1987), 361-394. MR 88j:55017
- 3.
- A. K. Bousfield and D. M. Kan, A second quadrant homotopy spectral sequence, Trans. A.M.S. 177(1973), 305-318. MR 51:9063
- 4.
- ______ , Homotopy Limits, Completions, and Localizations, Lecture Notes in Mathematics 304, Springer-Verlag, 1972. MR 51:1825
- 5.
- F. Cohen, T. Lada, and J. May, The Homology of Iterated Loop Spaces, Lecture Notes in Mathematics 533, Springer-Verlag. MR 55:9096
- 6.
- A. Dold, Über die Steenrodschen Kohomologieoperationen, Ann. of Math. 73(1961), 258-294. MR 23:A646
- 7.
- W. Dwyer, Higher divided squares in second quadrant spectral sequences, Trans. A.M.S. 260(1980), 437-447. MR 81f:55022
- 8.
- J. P. May, A general algebraic approach to Steenrod operations, The Steenrod Algebra and its Applications, Lecture Notes in Mathematics 168, Springer-Verlag (1970), 153-231. MR 43:6915
- 9.
- ______ , The Geometry of Iterated Loop Spaces, Lecture Notes in Mathematics 271, Springer-Verlag, 1972. MR 54:8623b
- 10.
- J. McClure, Private communication, November 1993.
- 11.
- D. Rector, Steenrod operations in the Eilenberg-Moore spectral sequence, Comment. Math. Helv. 45 (1970), 540-552. MR 43:4040
- 12.
- W. Singer, Steenrod squares in spectral sequences I, II, Trans. A.M.S. 175(1973), 327-336, 337-353. MR 47:7739
- 13.
- L. Smith, On the Kunneth theorem I, Math. Zeit. 116 (1970), 94-140. MR 44:3315
- 14.
- ______ , Steenrod squares in spectral sequences: the cohomology of Hopf algebra extensions and of classifying spaces, preprint, Fordham University (1997)
- 15.
- J. Turner, Looping Bousfield-Kan Towers, in preparation
- 16.
- ______ , Operations and spectral sequences II, III, in preparation
- 17.
- C. Weibel, An Introduction to Homological Algebra, Cambridge Studies in Advanced Mathematics 38, Cambridge University Press, 1995. MR 95f:18001
Similar Articles:
Retrieve articles in Transactions of the American Mathematical Society
with MSC
(1991):
18G40, 55S05, 55U15,
18G30, 55S10, 55S12, 55T10, 55T20
Retrieve articles in all Journals with MSC
(1991):
18G40, 55S05, 55U15,
18G30, 55S10, 55S12, 55T10, 55T20
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:
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
Copyright of article:
Copyright
1998,
American Mathematical Society
|
Comments: webmaster@ams.org