论文标题
算术群的共同学的入门计算
Introductory computations in the cohomology of arithmetic groups
论文作者
论文摘要
本文介绍了一种计算机辅助计算的方法，该计算是算术组的共同点。它通过强调同质性和扰动技术而不是细胞细分来补充有关该主题的现有文献，因为它是实施在计算机拓扑结构上实施的工具，这些工具无法保留细胞结构，而不仅仅是计算整体式的同学，而不仅仅是在大prime上进行合理的共同体或同学。特别是，本文介绍并充分讲述了计算Hecke操作员的算法，以$ sl_2（\ slbb z）$的一致性子组的整体cuspidal协同学$γ$ $γ$ quast $ sl_2（\ mathbb z）$，然后在特殊线性组$ sl_2的算法中进行部分讲述。 $ {\ cal o} _d $。该方法也与$ sl_m（{\ cal o} _d）$，$ M \ ge 2 $的一致性子组的计算相关。
This paper describes an approach to computer aided calculations in the cohomology of arithmetic groups. It complements existing literature on the topic by emphasizing homotopies and perturbation techniques, rather than cellular subdivision, as the tools for implementing on a computer topological constructions that fail to preserve cellular structures Furthermore, it focuses on calculating integral cohomology rather than just rational cohomology or cohomology at large primes. In particular, the paper describes and fully implements algorithms for computing Hecke operators on the integral cuspidal cohomology of congruence subgroups $Γ$ of $SL_2(\mathbb Z)$, and then partially implements versions of the algorithms for the special linear group $SL_2({\cal O}_d)$ over various rings of quadratic integers ${\cal O}_d$. The approach is also relevant for computations on congruence subgroups of $SL_m({\cal O}_d)$, $m\ge 2$.
