Topological K-theory of the integers at the prime 2, by Luke Hodgkin

Recent results of Voevodsky and others have effectively led to the proof of the Lichtenbaum-Quillen conjectures at the prime 2, and consequently made it possible to determine the 2-local homotopy type of the K-theory spectra for various number rings. The basic case is that of BGL(Z); in this note we use these results to determine the 2-local (topological) K-theory of the space BGL(Z), which can be described as a completed tensor product of two quite simple components; one corresponds to a real `image of J' space, the other to BBSO.

This is a revised and improved version of a previous paper with a similar title (these archives, no. 211), which it replaces.

Luke Hodgkin <>