Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-20T14:20:38.806Z Has data issue: false hasContentIssue false
  • English
  • Français

A localization theorem in homological algebra

Published online by Cambridge University Press:  24 October 2008

Haynes R. Miller
Haynes R. Miller
Affiliation:
Harvard University
Get access Rights & Permissions [Opens in a new window]

Extract

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

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 73 - 84
Copyright
Copyright © Cambridge Philosophical Society 1978

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Adams, J. F.A finiteness theorem in homological algebra. Proc. Cambridge Philos. Soc. 57 (1961), 31–36.CrossRefGoogle Scholar
(2)Adams, J. F.A periodicity theorem in homological algebra. Proc. Cambridge Philos. Soc. 62 1966, 365–377.CrossRefGoogle Scholar
(3)Anderson, D. W. and Davis, D. W.A vanishing theorem in homological algebra. Comment Math. Helv. 48 (1973), 318–327.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), 457–479.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), 199–236.CrossRefGoogle Scholar
(8)Husemoller, D., Moore, J. C. and Stasheff, J.Differential homological algebra and homogeneous spaces. J. Pure and Appl. Alg. 5 (1974), 113–185.CrossRefGoogle Scholar
(9)Mahowald, M.The order of the image of the J-homomorphism. Bull. Amer. Math. Soc. 76 1970, 1310–1313.CrossRefGoogle Scholar
(10)Massey, W. S. and Peterson, F. P.The cohomology structure of certain fibre spaces: I. Topology 4 (1965), 47–65.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), 433–447.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), 469–516.CrossRefGoogle Scholar
(13)Milnor, J. and Moore, J. C.On the structure of Hopf algebras. Ann. of Math. 81 (1965), 211–264.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), 827–913.CrossRefGoogle Scholar
(16)Steenrod, N. E. and Epstein, D. B. A.Cohomology operations (Princeton University Press, 1962).Google Scholar