E_n ring spectrum

\({\mathbb{E}}_\infty\) ring spectra

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More or less the same thing as a \(\Gamma{\hbox{-}}\)space a la Segal. Can produce these from an H-space

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Relation to surgery:

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Relation to structured ring spectra and symmetric spectra attachments/Pasted%20image%2020220316202343.png

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ring spectra

E_n ring
perfect complexes

\(M\) is a compact object in the infty-category of module spectra over a ring spectrum.
factorization homology

Descriptions of the factorization homology of free E_n algebra and of \(E_n{\hbox{-}}\)enveloping algebras of Lie algebras are known.
derived algebraic geometry

E_infty rings
Talbot Talk 2

First case of a purely symplectic construction of an \(E_\infty{\hbox{-}}\)algebra! See E_infty algebra

Question: can one symplectically construct certain \(E_\infty\) maps, e.g. \({\mathbb{S}}, {\mathbb{S}}{ \left[ { \scriptstyle \frac{1}{p} } \right] }\).? See E_infty.
Morava E theory

It’s an E-infty ring spectrum with coefficients in Witt vectors.

E_infty ring spectrum.
May recognition principle

E_infty
H-space

Can upgrade to an E_infty space.