On the ku-homology of certain classifying spaces

TL;DR

This paper computes the ku-homology of specific product groups and demonstrates that it encapsulates all complex bordism information, providing explicit generators for annihilators of key classes.

Contribution

It offers explicit calculations of ku-homology for certain groups and links it to complex bordism, introducing generators for annihilators of important classes.

Findings

ku-homology contains all complex bordism information for these groups

Constructed generators of the annihilator of the ku-toral class

Generated elements also annihilate the BP-toral class

Abstract

We calculate the ku-homology of the groups Z/p^n X Z/p and Z/p^2 X Z/p^2. We prove that for this kind of groups the ku-homology contains all the complex bordism information. We construct a set of generators of the annihilator of the ku-toral class. These elements also generates the annihilator of the BP-toral class.