Abstract: The Steenrod operations were first conceived as operations on the cohomology of topological spaces with coefficients in ℤ/pℤ for some prime p. The cohomology of a finite group G can be viewed as the cohomology of its classifying space BG, and hence the Steenrod operations apply to the mod-p cohomology of G. There is also an algebraic definition of the Steenrod operations which can be invoked when we wish to avoid a topological construction. The algebraic construction is based on the observation that the diagonal approximations for resolutions are cocommutative only up to homotopy. The absence of strict cocommutativity allows us to define new cocycles from the noncommutativity of old ones.
Publication Year: 2003
Publication Date: 2003-01-01
Language: en
Type: book-chapter
Indexed In: ['crossref']
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