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Topological $K$-theory of the Integers at the Prime 2

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-homotopy type of the $K$-theory spectra for various number rings. The basic case is that of $ BGL({\Bbb Z})$; in this note we use these results to determine the 2-local (topological) $K$-theory of the space $BGL({\Bbb Z})$, 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 $BBSO$.

Homology, Homotopy and Applications, Vol. 2, 2000, No. 9, pp. 119-126

http://www.rmi.acnet.ge/hha/volumes/2000/n9/n9.dvi (ps, dvi.gz, ps.gz)
ftp://ftp.rmi.acnet.ge/pub/hha/volumes/2000/n9/n9.dvi (ps, dvi.gz, ps.gz)