H-infinity is not E-infinity

We provide an example of a spectrum over S^0 with an H_\infty structure which does not rigidify to an E_3 structure. It follows that in the category of spectra over S^0 not every H_\infty ring spectrum comes from an underlying E_\infty ring spectrum. After comparing definitions, we obtain this examp...

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Bibliographic Details
Published in:arXiv.org 2014-04
Main Author: Noel, Justin
Format: Article
Language:English
Subjects:
H infinity
Online Access:Get full text
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Summary:We provide an example of a spectrum over S^0 with an H_\infty structure which does not rigidify to an E_3 structure. It follows that in the category of spectra over S^0 not every H_\infty ring spectrum comes from an underlying E_\infty ring spectrum. After comparing definitions, we obtain this example by applying \Sigma^\infty_+ to the counterexample to the transfer conjecture constructed by Kraines and Lada.
ISSN:2331-8422