A rigidity theorem for group extensions
A rigidity theorem for group extensions
复制标题
群扩张的刚性定理
DOI：
10.1007/s000130050371
复制
发表时间：
1999
影响因子：
0.6
通讯作者：
F. Johnson
中科院分区：
文献类型：
--
作者：
F. Johnson
我们考虑作为迭代表面纤维的基本群而出现的离散群的类别；也就是说，从一系列纤维化获得的复合物，其中所有碱基和初始纤维都是双曲表面。从理论上讲，这对应于研究双曲曲面群的迭代扩展类。在[4]中，对于单个扩展的情况，我们推测并部分确定任何群都不能由超过有限数量的此类扩展产生。在这里，我们表明结果具有完全的普遍性。正如 [4] 中所述，结果与 Parshin [7] 和 Arakelov [1] 对于纤维（复）代数曲面的刚性定理有很强的亲和力。
We consider the class of discrete groups which arise as fundamental groups of iterated surface fibrations; that is, of complexes obtained from a sequence of fibrations in which all bases and the initial fibre are hyperbolic surfaces. Group theoretically, this corresponds to studying the class of iterated extensions of hyperbolic surface groups. In [4], for the case of a single extension we conjectured and partially established that no group can arise from more than a finite number of such extensions. Here we show that the result holds in complete generality. As remarked in [4], the result has a strong affinity with the rigidity theorems of Parshin [7] and Arakelov [1] for fibred (complex) algebraic surfaces.