A quick proof of the rational Hurewicz theorem and a computation of the rational homotopy groups of spheres
A quick proof of the rational Hurewicz theorem and a computation of the rational homotopy groups of spheres
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有理 Hurewicz 定理的快速证明和球面有理同伦群的计算
DOI：
10.1017/s0305004103007114
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发表时间：
2004
影响因子：
0.8
通讯作者：
M. Kreck
中科院分区：
文献类型：
--
作者：
S. Klaus;M. Kreck
我们给出了有理 Hurewicz 定理的基本证明，并计算了 Eilenberg-MacLane 空间的有理上同调群和球面的有理同伦群。我们不使用Serre谱序列，只假设经典的Hurewicz定理，并给出有理Gysin和Wang长精确序列的简短证明，并将其归纳应用于Eilenberg-MacLane空间的路径纤维化。
We give an elementary proof of the rational Hurewicz theorem and compute the rational cohomology groups of Eilenberg–MacLane spaces and the rational homotopy groups of spheres. Instead of using the Serre spectral sequence, we only assume the classical Hurewicz theorem, and give a short proof of the rational Gysin and Wang long exact sequences, which are applied inductively to the path fibration of Eilenberg–MacLane spaces.