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Steenrod’s operations in simplicial Bredon-Illman cohomology with local coefficients. (English) Zbl 1223.55001
S. Gitler constructed reduced power operations in cohomology with local coefficients in [Am. J. Math. 85, 156–188 (1963; Zbl 0131.38006)]. Inspired by this work, the present authors use an algebraic approach to Steenrod operations, due to J. P. May [Steenrod Algebra Appl., Lect. Notes Math. 168, 153–231 (1970; Zbl 0242.55023)], and by using the equivariant description of Eilenberg, they reproduce Steenrod’s reduced power operations in simplicial Bredon-Illman cohomology of a one vertex \(G\)-Kan complex where the equivariant local coefficients take values in \(\mathbb{Z}_p\)-algebras, for a prime \(p>2\).

MSC:
55N25 Homology with local coefficients, equivariant cohomology
55U10 Simplicial sets and complexes in algebraic topology
55N91 Equivariant homology and cohomology in algebraic topology
57S99 Topological transformation groups
55S05 Primary cohomology operations in algebraic topology
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