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A localization theorem in homological algebra

Published online by Cambridge University Press:  24 October 2008

Haynes R. Miller
Affiliation:
Harvard University

Extract

In (1), J. F. Adams showed that for p odd, the Adams E2-term for a sphere, , is zero for st ≤ (2p − 1)s − 1, while is the one-dimensional vector space generated by where corresponds to the Bockstein.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Adams, J. F.A finiteness theorem in homological algebra. Proc. Cambridge Philos. Soc. 57 (1961), 3136.CrossRefGoogle Scholar
(2)Adams, J. F.A periodicity theorem in homological algebra. Proc. Cambridge Philos. Soc. 62 1966, 365377.CrossRefGoogle Scholar
(3)Anderson, D. W. and Davis, D. W.A vanishing theorem in homological algebra. Comment Math. Helv. 48 (1973), 318327.CrossRefGoogle Scholar
(4)Bousfield, A. K. and Curtis, E. B.A spectral sequence for the homotopy of nice spaces. Trans. Amer. Math. Soc. 151 (1970), 457479.CrossRefGoogle Scholar
(5)Cartan, H.DGA-modules (Suite): Notion de construction, exp. 3, Seminaire H. Cartan, 1954/1955 Paris.Google Scholar
(6)Cartan, H. and Eilenbebg, S.Homological algebra (Princeton University Press, 1956).Google Scholar
(7)Eilenberg, S. and Moore, J. C.Homology and fibrations. I. Coalgebras, cotensor product and its derived functors. Comment Math. Helv. 40 (1966), 199236.CrossRefGoogle Scholar
(8)Husemoller, D., Moore, J. C. and Stasheff, J.Differential homological algebra and homogeneous spaces. J. Pure and Appl. Alg. 5 (1974), 113185.CrossRefGoogle Scholar
(9)Mahowald, M.The order of the image of the J-homomorphism. Bull. Amer. Math. Soc. 76 1970, 13101313.CrossRefGoogle Scholar
(10)Massey, W. S. and Peterson, F. P.The cohomology structure of certain fibre spaces: I. Topology 4 (1965), 4765.CrossRefGoogle Scholar
(11)Miller, H. R. and Ravenel, D. C.Morava stabilizer algebras and the localization of Novikov's E 2-term. Duke J. Math. 44 (1977), 433447.CrossRefGoogle Scholar
(12)Miller, H. R., Ravenel, D. C. and Wilson, W. S.Periodic phenomena in the Adams-Novikov spectral sequence. Ann. of Math. 106 (1977), 469516.CrossRefGoogle Scholar
(13)Milnor, J. and Moore, J. C.On the structure of Hopf algebras. Ann. of Math. 81 (1965), 211264.CrossRefGoogle Scholar
(14)Morava, J. Extensions of cobordism comodules. (To appear.)Google Scholar
(15)Novikov, S. P.The methods of algebraic topology from the viewpoint of cobordism theory. Math. USSR Izvestija 1 (1967), 827913.CrossRefGoogle Scholar
(16)Steenrod, N. E. and Epstein, D. B. A.Cohomology operations (Princeton University Press, 1962).Google Scholar