Steenrod operations on bar complex

Abstract

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.

14pages

References in corpus (2)

• Combinatorial operad actions on cochains
• On the Multiplicative Structure of Topological Hochschild Homology