球谱的代数K理论的同伦群
The homotopy groups of the algebraic K-theory of the sphere spectrum
摘要：
根据$K(\mathbb Z)$的同伦群、${\mathbb C}P^\infty_{-1}$的同伦群和$\mathbb S$的同伦群，计算了$π_*K(\mathbb S)[1/2]$、$K(\mathbb S)$的远离2的同伦群.这是建立在瓦尔德豪森的工作基础上的，他计算了有理同伦群（建立在奎伦和博雷尔的工作基础上）和罗格尼斯的工作基础上，罗格尼斯根据${\mathbb C}P^\infty_{-1}$的同伦群和$\mathbb S$的同伦群计算了在正则素数处的群。
英文摘要：
We calculate $π_*K(\mathbb S)[1/2]$, the homotopy groups of $K(\mathbb S)$ away from 2, in terms of the homotopy groups of $K(\mathbb Z)$, the homotopy groups of ${\mathbb C}P^\infty_{-1}$, and the homotopy groups of $\mathbb S$. This builds on the work of Waldhausen, who computed the rational homotopy groups (building on work of Quillen and Borel) and Rognes, who calculated the groups at regular primes in terms of the homotopy groups of ${\mathbb C}P^\infty_{-1}$, and the homotopy groups of $\mathbb S$.
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