Steenrod operations on bar complex

2011/08/23 by Syunji Moriya, Moriya, Syunji
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.AT

paper · pdf · doi:10.48550/arxiv.1108.4495

14pages

arxiv created 2011/08/23 · openalex publication_date 2011/08/23 · arxiv updated 2011/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a chain map of the form \E(k)⊗ BA^{⊗ k}\longrightarrow BA, where \E is a combinatorial E_∞-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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