The spectral sequence of an extraordinary cohomology theory

Autor:	C. R. F. Maunder
Rok vydání:	1963
Předmět:	Combinatorics Mathematics::K-Theory and Homology General Mathematics Existential quantification Dimension (graph theory) Spectral sequence Space (mathematics) Mathematics::Algebraic Topology Axiom Cohomology Mathematics
Zdroj:	Mathematical Proceedings of the Cambridge Philosophical Society. 59:567-574
ISSN:	1469-8064 0305-0041
DOI:	10.1017/s0305004100037245
Popis:	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.
Databáze:	OpenAIRE
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