The connective -theory of the Eilenberg–MacLane space

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...

Full description

Saved in:
Bibliographic Details
Published in:Glasgow mathematical journal 2024-01, Vol.66 (1), p.1-33
Main Authors: Davis, Donald M., Wilson, W. Stephen
Format: Article
Language:English
Subjects:
Algebra
Homology
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary: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.
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089523000423