Filtered spaces admitting spectral sequence operations.
Lewis Shilane
Source: Pacific J. Math. Volume 62, Number 2 (1976), 569-585.
Primary Subjects: 55G10
Full-text: Open access
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.pjm/1102867739
Zentralblatt MATH identifier:
0361.55015
Mathematical Reviews number (MathSciNet):
MR0431167
References
[4] Products and operations.It should be clear that the diagonal approximations and equivariant diagonal approximations for quasi-products enable us to define products and Steenrod operations inthe spectral sequences.We mention a few of the details involved in the construction of the spectral operations, which parallels the construction of Steenrod squares for regular CW-complexes, and also give some proper- ties of the operations.
[1] The cellular cochain complex is replaced by the E level of the spectral sequence: Epq=Hp+q(Qp,Qp-).
[4] If /: Q - Q is a cellular fiber map which factors through the projection q on each quasi-cell of Q, then the 5' commute with /* on En (r^2).
[1] George E. Cooke and Ross L. Finney, Homology of cell complexes, Princeton Univ. Press, Princeton, N.J., 1967.
Mathematical Reviews (MathSciNet):
MR36:2142
Zentralblatt MATH:
0173.25701
[2] David L. Rector, Steenrod operations in the Eilenberg-Moore spectral sequence, Comm. Math. Helv., 45 (1970), 540-552.
Mathematical Reviews (MathSciNet):
MR43:4040
Zentralblatt MATH:
0209.27501
[3] William M. Singer, Steenrod squares in spectral sequences, I, II, unpublished notes, Dept. of Mathematics, Boston College, Chestnut Hill, Mass.
[4] Larry Smith, On the constructionof the Eilenberg -Moore spectral sequence,Bull. Amer. Math. Soc, 75 (1969), 873-878.
Mathematical Reviews (MathSciNet):
MR40:3551
Zentralblatt MATH:
0177.51403
[5] Larry Smith,Lectures on the Eilenberg-Moore spectral sequence,Lecture Notes in Mathematics no. 134. Springer-Verlag, New York, 1970.
Mathematical Reviews (MathSciNet):
MR43:1191
Zentralblatt MATH:
0197.19702
[6] Norman E. Steenrod, A convenient category of topological spaces, Michigan J. Math., 14 (1967), 133-152.
Mathematical Reviews (MathSciNet):
MR35:970
Zentralblatt MATH:
0145.43002
[7] Norman E. Steenrod, Milgram's classifying space of a topological group, Topology, 7 (1968), 349-368.
Mathematical Reviews (MathSciNet):
MR38:1675
Zentralblatt MATH:
0177.51601
Pacific Journal of Mathematics
