虚二次整数$PSL_2$与非平凡类群的积分同调
The integral homology of $PSL_2$ of imaginary quadratic integers with non-trivial class group
摘要：
我们表明，由Floege描述的细胞复合体允许确定的Bianchi组$PSL_2(O_{-m})$，其中$O_{-m}$是一个虚二次数域$\rationals[\sqrt{-m}]$的整数环的平方自由自然数$m$的积分同源。我们用它来计算m = 5，6，10，13和15的情况下的非平凡类群的积分同调的$PSL_2(O_{-m})$，这是以前只知道的情况下，m = 1，2，3，7和11的平凡类群。
英文摘要：
We show that a cellular complex described by Floege allows to determine the integral homology of the Bianchi groups $PSL_2(O_{-m})$, where $O_{-m}$ is the ring of integers of an imaginary quadratic number field $\rationals[\sqrt{-m}]$ for a square-free natural number $m$. We use this to compute in the cases m = 5, 6, 10, 13 and 15 with non-trivial class group the integral homology of $PSL_2(O_{-m})$, which before was known only in the cases m = 1, 2, 3, 7 and 11 with trivial class group.
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