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Adams-type maps are not stable under composition

We give a simple counterexample to the plausible conjecture that Adams-type maps of ring spectra are stable under composition. We then show that over a field, this failure is quite extreme, as any map of \(\mathbb{E}_{\infty}\)-algebras is a transfinite composition of Adams-type maps.

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Bibliographic Details
Published in:arXiv.org 2022-02
Main Authors: Burklund, Robert, Levy, Ishan, PstrÄ…gowski, Piotr
Format: Article
Language:English
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Online Access:Get full text
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Summary:We give a simple counterexample to the plausible conjecture that Adams-type maps of ring spectra are stable under composition. We then show that over a field, this failure is quite extreme, as any map of \(\mathbb{E}_{\infty}\)-algebras is a transfinite composition of Adams-type maps.
ISSN:2331-8422