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

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

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