论文标题
在Equivariant $ k $ - 和$ ko $ - 某些特殊线性群体的知名度
On the equivariant $K$- and $KO$-homology of some special linear groups
论文作者
论文摘要
我们计算分类空间的Equivariant $ ko $ - 理论，用于$ \ textrm {sl} _3（\ Mathbb {z}）$和$ \ textrm {gl} _3（\ m athbb {z}}）$。我们还计算了Bredon同源性和Equivariant $ K $ - 分类空间的$ \ textrm {psl} _2（\ Mathbb {Z} [\ frac {1} {1} {p} {p}]））$ and和$ \ textrm {sl} _2（\ mathbb {z} [\ frac {1} {p}]）$对于每个prime $ p $。最后，我们证明了不稳定的Gromov-lawson-Rosenberg猜想，这些群体的最大有限亚组是奇数且具有周期性的共同体学。
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.
