论文标题
比安奇的其他对称性
Bianchi's additional symmetries
论文作者
论文摘要
在2012年的“ Comptes Rendus Math {é} Matique”中，作者确实试图回答Jean-Pierre Serre的问题。最近宣布，该答案的范围需要进行调整，本文中给出了此调整的细节。最初的问题是以下内容。考虑想象中的二次数字字段中的整数o，以及SL 2（O）对双曲线3空间商的Borel-Serre紧凑型。考虑将边界连接到Borel-Serre紧凑型时，请考虑同源物引起的地图$α$。一个人如何确定$α$的内核？ Serre使用了全球拓扑论点，并获得了$α$的内核等级。他添加了一个问题，该核恰恰是什么。
In a 2012 note in Comptes Rendus Math{é}matique, the author did try to answer a question of Jean-Pierre Serre; it has recently been announced that the scope of that answer needs an adjustment, and the details of this adjustment are given in the present paper. The original question is the following. Consider the ring of integers O in an imaginary quadratic number field, and the Borel-Serre compactification of the quotient of hyperbolic 3-space by SL 2 (O). Consider the map $α$ induced on homology when attaching the boundary into the Borel-Serre compactification. How can one determine the kernel of $α$ (in degree 1) ? Serre used a global topological argument and obtained the rank of the kernel of $α$. He added the question what submodule precisely this kernel is.
