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arXiv · 2004.08199

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

Sam Hughes
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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.

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BibTeXRIS

Sam Hughes. 2020-04-17. On the equivariant $K$- and $KO$-homology of some special linear groups. https://doi.org/10.2140/agt.2021.21.3483

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