nLab
iterated loop space

Contents

Idea

A multiple loop space.

A grouplike E-k algebra in Top.

An iterated loop space object in Top.

(∞,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, Infinite loop space theory, Bull. Amer. Math. Soc. Volume 83, Number 4 (1977), 456-494. (Euclid)

    Infinite loop space theory revisited (pdf)

  • John Adams, Infinite loop spaces, Herrmann Weyl lectures at IAS, Princeton University Press (1978)

  • Peter May, The uniqueness of infinite loop space machines, Topology, vol 17, pp. 205-224 (1978) (pdf)

Section 5.1.3 of

Revised on June 27, 2012 15:06:31 by Urs Schreiber (131.174.40.150)