We calculate pi K-*(S) circle times Z[1/2], the homotopy groups of K(S) away from 2, in terms of the homotopy groups of K(Z), the homotopy groups of CP-1 infinity and the homotopy groups of S. This builds on work of Waldhausen, who computed the rational homotopy groups (building on work of Quillen and Borel) and Rognes, who calculated the groups at odd regular primes in terms of the homotopy groups of CP-1 infinity and the homotopy groups of S.
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机译：我们计算PI K - *（S）圆形时间Z [1/2]，k（s）的同态组，即K（z）的同型均多组，CP-1无限远的同型组 和S.的同态群体建立在Waldhausen的工作，他们计算了理性同型群体（在Quillen和Borel的工作）和Rognes的基础上，他们在CP-1的同态群体中以奇数常规素数计算群体 Infinity和S的同型群体
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