We compute $ku^*\left(K\!\left({\mathbb{Z}}_p,2\right)\right)$ and $ku_*\left(K\!\left({\mathbb{Z}}_p,2\right)\right)$, the connective $KU$-cohomology and connective $KU$-homology groups of the mod-$p$ Eilenberg–MacLane space $K\!\left({\mathbb{Z}}_p,2\right)$, using the Adams spectral sequence. We obtain a striking interaction between $h_0$-extensions and exotic extensions. The mod-$p$ connective $KU$-cohomology groups, computed elsewhere, are needed in order to establish higher differentials and exotic extensions in the integral groups.

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连接词

我们计算$ku^*\left(K\!\left({\mathbb{Z}}_p,2\right)\right)$和$ku_*\left(K\!\left({\mathbb{Z }}_p,2\right)\right)$，mod- $ p$ Eilenberg –MacLane 空间$ K\!\left({\mathbb { Z}}_p,2\right)$，使用 Adams 谱序列。我们在$h_0$扩展和外来扩展之间获得了惊人的交互。为了在积分群中建立更高的微分和奇异扩展，需要在别处计算的mod- $p$连接$KU$ -上同调群。