H-infinity is not E-infinity

2009/10/19 by Justin Noel, Noel, Justin
Mathematics · #55P42 #55P48 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0910.3566

openalex publication_date 2009/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide an example of a spectrum over S⁰ with an H_∞ structure which does not rigidify to an E₃ structure. It follows that in the category of spectra over S⁰ not every H_∞ ring spectrum comes from an underlying E_∞ ring spectrum. After comparing definitions, we obtain this example by applying Σ^∞₊ to the counterexample to the transfer conjecture constructed by Kraines and Lada.

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