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The spectral sequence of an extraordinary cohomology theory

  • C. R. F. Maunder (a1)

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Given an ‘extraordinary cohomology theory’, that is, a cohomology theory satisfying all the axioms of Eilenberg and Steenrod (7) except the dimension axiom, it is well known that there exists a spectral sequence relating the ordinary cohomology of a space with the extraordinary theory (see, for example, (3) in the case of K*(X)). Obviously, it would be useful to know the differentials in this spectral sequence, and it is the purpose of this paper to identify them in terms of cohomology operations defined by certain k-invariants. We shall make use of E. H. Brown's recent theorem (5) on the representability of extraordinary cohomology theories, to construct a second spectral sequence, in which the differentials are readily identifiable, which we shall prove is isomorphic to the usual one.

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COPYRIGHT: © Cambridge Philosophical Society 1963

References

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  • Cited by 9

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The spectral sequence of an extraordinary cohomology theory

  • C. R. F. Maunder (a1)

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