Rognes and Weibel used Voevodsky's work on the Milnor conjecture to deduce the strong Dwyer-Friedlander form of the Lichtenbaum-Quillen conjecture at the prime 2. In consequence (the 2-completion of) the classifying space for algebraic K -theory of the integers [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] can be expressed as a fiber product of well-understood spaces BO and [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="02i" /] over BU . Similar results are now obtained for Hermitian K -theory and the classifying spaces of the integral symplectic and orthogonal groups. For the integers [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="03i" /], this leads to computations of the 2-primary Hermitian K -groups and affirmation of the Lichtenbaum-Quillen conjecture in the framework of Hermitian K -theory.
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Berrick et al. (2005) studied this question.