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cohomology ring

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Given any generalized (Eilenberg-Steenrod) cohomology theory EE, then for each topological space XX, there is, by definition, the graded abelian group

E (X)Ab . E^\bullet(X) \in Ab^{\mathbb{Z}} \,.

This is the EE-cohomology group of XX. Now if EE is a multiplicative cohomology theory, then these groups inherit the structure of rings. As such

E (X)Ring E^\bullet(X) \in Ring^{\mathbb{Z}}

is the EE-cohomology ring of XX.

Analogously for various suitable generalizations of the nature of EE and XX (see at generalized cohomology).

Revised on May 27, 2016 10:11:38 by Urs Schreiber (131.220.184.222)