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Sep 20, 2014 at 4:27 vote accept Jonathan Beardsley
Oct 25, 2013 at 13:01 answer added Oscar Randal-Williams timeline score: 7
Oct 25, 2013 at 8:02 comment added Justin Noel I am not sure that it has exactly what you are looking for, but Neil Strickland's thesis contains an astounding amount of information about the homology of K-theoretic spaces, such as those in your question. Even if it does not answer your question, it might help you with many related questions.
Oct 25, 2013 at 2:58 history asked Jonathan Beardsley CC BY-SA 3.0