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The connective
$K$-theory of the Eilenberg–MacLane space 
$K\!\left({\mathbb{Z}}_p,\textrm{2}\right)$
- Part of
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- Journal:
- Glasgow Mathematical Journal / Volume 66 / Issue 1 / January 2024
- Published online by Cambridge University Press:
- 11 December 2023, pp. 188-220
- Print publication:
- January 2024
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- Article
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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.
