H-infinity is not E-infinity

Abstract

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 Σ^\infty_+ to the counterexample to the transfer conjecture constructed by Kraines and Lada.

This paper was long ago accepted for publication in the Proceedings of the 4th Arolla Conference. This is the publication version

References in corpus (1)

• What precisely are $E_{\infty }$ ring spaces and $E_{\infty }$ ring spectra?

Cited by in corpus (2)

• A note on H_infinity structures
• $G_{\infty }$-ring spectra and Moore spectra for $\beta$-rings