Infinite loop space machine explained

In topology, a branch of mathematics, given a topological monoid X up to homotopy (in a nice way), an infinite loop space machine produces a group completion of X together with infinite loop space structure. For example, one can take X to be the classifying space of a symmetric monoidal category S; that is,

X = BS . Then the machine produces the group completion BS \to K(S) . The space K(S) may be described by the K-theory spectrum of S.

In 1977 Robert Thomason proved theequivalence of all infinite loop space machines^[1] (he was just 25 years old at the moment.) He published this result next year in a joint paper with John Peter May.

References

• J. P. May and R. Thomason The uniqueness of infinite loop space machines

Notes and References

1. https://www.ams.org/notices/199608/comm-thomason.pdf Charles Weibel, "Robert W. Thomason 1952--1995", Notices of the AMS, 1996, Volume 43, Number 8