Infinite loop space machine
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, . Then the machine produces the group completion . The space may be described by the K-theory spectrum of S.
In 1977 Robert Thomason proved the equivalence 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 Jon Peter May.
References
- ^ Charles Weibel, "Robert W. Thomason 1952--1995", Notices of the AMS, 1996, Volume 43, Number 8
- J. P. May and R. Thomason The uniqueness of infinite loop space machines
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