nLab
E-infinity space

Contents

Definition

An E E_\infty-space is an E-∞ algebra in Top.

Properties

Grouplike E E_\infty-spaces are equivalently infinite loop spaces. See there for more details.

(∞,1)-operad∞-algebragrouplike versionin Topgenerally
A-∞ operadA-∞ algebra∞-groupA-∞ space, e.g. loop spaceloop space object
E-k operadE-k algebrak-monoidal ∞-groupiterated loop spaceiterated loop space object
E-∞ operadE-∞ algebraabelian ∞-groupE-∞ space, if grouplike: infinite loop space \simeq Γ-spaceinfinite loop space object
\simeq connective spectrum\simeq connective spectrum object
stabilizationspectrumspectrum object

References

  • Peter May with contributions by Frank Quinn, Nigel Ray and Jorgen Tornehave, E E_\infty-Ring spaces and E E_\infty ring spectra (pdf)

Revised on November 14, 2013 00:20:08 by Urs Schreiber (82.169.114.243)