Geodesic
Topological $K$-theory of the integers at the prime 2
Homology, homotopy, and applications, Tome 2 (2000) no. 1, pp. 119-126.

Voir la notice de l'article provenant de la source International Press of Boston

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 $BGL(\mathbb{Z})$; in this note we use these results to determine the 2-local (topological) $K$-theory of the space $BGL(\mathbb{Z})$, 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 $BBSO$.
DOI : 10.4310/HHA.2000.v2.n1.a9
Classification : 19Dxx, 55N15, 55P15
Keywords: $K$-theory, general linear group of integers, Rothenberg-Steenrod spectral sequence, Bousfield localization 
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     author = {Luke Hodgkin},
     title = {Topological $K$-theory of the integers at the prime 2},
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     pages = {119--126},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2000.v2.n1.a9/}
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Luke Hodgkin. Topological $K$-theory of the integers at the prime 2. Homology, homotopy, and applications, Tome 2 (2000) no. 1, pp. 119-126. doi : 10.4310/HHA.2000.v2.n1.a9. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2000.v2.n1.a9/

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