# On the equivariant K- and KO-homology of some special linear groups

Hughes, S

## Journal:

Algebraic and Geometric Topology

## Last Updated:

2021-11-12T09:54:18.413+00:00

## abstract:

We compute the equivariant $KO$-homology of the classifying space for proper
actions of $\textrm{SL}_3(\mathbb{Z})$ and $\textrm{GL}_3(\mathbb{Z})$. We also
compute the Bredon homology and equivariant $K$-homology of the classifying
spaces for proper actions of $\textrm{PSL}_2(\mathbb{Z}[\frac{1}{p}])$ and
$\textrm{SL}_2(\mathbb{Z}[\frac{1}{p}])$ for each prime $p$. Finally, we prove
the Unstable Gromov-Lawson-Rosenberg Conjecture for a large class of groups
whose maximal finite subgroups are odd order and have periodic cohomology.

1197273

Submitted

Journal Article