Steenrod operations on bar complex

Details Steenrod operations on bar complex Steenrod operations on bar complex

2011-08-23

arxiv.org/abs/1108.4495v1

Mathematics

Algebraic Topology

14pages

Scientific paper

We define a chain map of the form $\E(k)\otimes BA^{\otimes k}\longrightarrow BA$, where $\E$ is a combinatorial $E_\infty$-operad called the sequence operad, and $BA$ is the bar complex of an $\E$-algebra $A$. We see that Steenrod-type operations derived from the chain map are equal to the corresponding operations on the cohomology of the based loop space under an isomorphism.

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