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A localization theorem in homological algebra

  • Haynes R. Miller (a1)
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.

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(1)Adams, J. F.A finiteness theorem in homological algebra. Proc. Cambridge Philos. Soc. 57 (1961), 3136.
(2)Adams, J. F.A periodicity theorem in homological algebra. Proc. Cambridge Philos. Soc. 62 1966, 365377.
(3)Anderson, D. W. and Davis, D. W.A vanishing theorem in homological algebra. Comment Math. Helv. 48 (1973), 318327.
(4)Bousfield, A. K. and Curtis, E. B.A spectral sequence for the homotopy of nice spaces. Trans. Amer. Math. Soc. 151 (1970), 457479.
(5)Cartan, H.DGA-modules (Suite): Notion de construction, exp. 3, Seminaire H. Cartan, 1954/1955 Paris.
(6)Cartan, H. and Eilenbebg, S.Homological algebra (Princeton University Press, 1956).
(7)Eilenberg, S. and Moore, J. C.Homology and fibrations. I. Coalgebras, cotensor product and its derived functors. Comment Math. Helv. 40 (1966), 199236.
(8)Husemoller, D., Moore, J. C. and Stasheff, J.Differential homological algebra and homogeneous spaces. J. Pure and Appl. Alg. 5 (1974), 113185.
(9)Mahowald, M.The order of the image of the J-homomorphism. Bull. Amer. Math. Soc. 76 1970, 13101313.
(10)Massey, W. S. and Peterson, F. P.The cohomology structure of certain fibre spaces: I. Topology 4 (1965), 4765.
(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.
(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.
(13)Milnor, J. and Moore, J. C.On the structure of Hopf algebras. Ann. of Math. 81 (1965), 211264.
(14)Morava, J. Extensions of cobordism comodules. (To appear.)
(15)Novikov, S. P.The methods of algebraic topology from the viewpoint of cobordism theory. Math. USSR Izvestija 1 (1967), 827913.
(16)Steenrod, N. E. and Epstein, D. B. A.Cohomology operations (Princeton University Press, 1962).
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Mathematical Proceedings of the Cambridge Philosophical Society
  • ISSN: 0305-0041
  • EISSN: 1469-8064
  • URL: /core/journals/mathematical-proceedings-of-the-cambridge-philosophical-society
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