Topological K-theory of GL(Z) at the prime 2
Luke Hodgkin
Kings College, Strand, London, WC2R 2LS
lukec.hodkin@kcl.ac.uk
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 of 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.