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The homology of BO and some results about the Steenrod algebra

Published online by Cambridge University Press:  24 October 2008

Edgar H. Brown Jr
Affiliation:
Brandeis University, Lehigh University, Massachusetts Institute of Technology
Donald M. Davis
Affiliation:
Brandeis University, Lehigh University, Massachusetts Institute of Technology
Franklin P. Peterson
Affiliation:
Brandeis University, Lehigh University, Massachusetts Institute of Technology

Abstract

Some explicit formulae for the right coaction of A* on H*BO are given. As corollaries, closed formulae for χ(ξk) and other elements in A* are given.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

(1)Adams, J. F.On the groups J(X): II. Topology 3 (1965), 137171.CrossRefGoogle Scholar
(2)Adams, J. F.Operations of the nth kind in K-theory, and what we don't know about RP. London Math. Soc. Lecture Notes 11 (1972), 19.Google Scholar
(3)Adams, J. F. and Walker, G.On complex Stiefel manifolds. Proc. Cambridge Philos. Soc. 61 (1965), 81103.CrossRefGoogle Scholar
(4)Atiyah, M. F.Thom complexes. Proc. London Math. Soc. 11 (1961), 291310.CrossRefGoogle Scholar
(5)Browder, W.The Kervaire invariant of framed manifolds and its generalizations. Ann. of Math. 90 (1969), 157186.CrossRefGoogle Scholar
(6)Brown, E. H. Jr and Peterson, F. P.Relations among characteristics classes: I. Topology 3 (1964), 3952.CrossRefGoogle Scholar
(7)Brown, E. H. Jr and Peterson, F. P.H*mo as an algebra over the Steenrod algebra. Notas de Mat. y Simpoaia, vol. 1, pp. 1121 (Soc. Mat. Mexico, 1975).Google Scholar
(8)Davis, D. M.The antiautomorphism of the Steenrod algebra. Proc. Amer. Math. Soc. 44 (1974), 235236.CrossRefGoogle Scholar
(9)Milnor, J. W.The Steenrod algebra and its dual. Ann. of Math. 67 (1958), 150171.CrossRefGoogle Scholar
(10)Papastavrides, S. The Arf invariant of manifolds with few nonzero Stiefel-Whitney classes. (To appear.)Google Scholar
(11)Peterson, F. P.Characteristic classes and cobordism. Actes Congres Intern. Math. 1970, tome 2, pp. 121125.Google Scholar
(12)Thom, R.Espaces fibres en spheres et carres de Steenrod. Ann. Sci. École Norm. Sup. 69 (1952),109182.CrossRefGoogle Scholar