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, $X = BS$ . 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.

References

May, The uniqueness of infinite loop space machine

This article is issued from Wikipedia - version of the Saturday, January 25, 2014. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.