Noncoherence of some lattices in Isom ( H
Noncoherence of some lattices in Isom ( H
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Isom 中某些格子的非相干性 ( H
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Ernest Vinberg
中科院分区：
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作者：
Michael Kapovich;Leonid Potyagailo;Ernest Vinberg;Heiner Zieschang;Michael Kapovich;Leonid Potyagailo;Ernest Vinberg
本文的目的是证明双曲n-空间Hn（n > 3）的等距群Isom（Hn）中某些格族的非相干性。我们还记得，群G称为凝聚群，如果G的每一个生成子群都是群的群。众所周知，Isom（H2）和Isom（H3）中的所有格都是相干的。事实上，很容易证明每一个生成的Fuchsian群都是可表示的。P Scott [21]证明了3-流形群的凝聚性。Isom（H4）的几何有限非相干离散子群的第一个例子是由第一和第二作者[10]和第二作者[17，18]构造的。Bowditch和Mess [4]给出了Isom（H4）中非相干均匀格的一个例子。在下文中，我们将把Hn与双曲面{x：f（x）= −1}<$Rn+1的连通分支等同起来，
The aim of this paper is to prove noncoherence of certain families of lattices in the isometry group Isom(Hn) of the hyperbolic n–space Hn (n > 3). We recall that a group G is called coherent if every finitely generated subgroup of G is finitely presented. It is well known that all lattices in Isom(H2) and Isom(H3) are coherent. Indeed, it is easy to prove that every finitely generated Fuchsian group is finitely presented. The coherence of 3–manifold groups was proved by P Scott [21]. First examples of geometrically finite noncoherent discrete subgroups of Isom(H4) were constructed by the first and second author [10] and the second author [17, 18]. An example of noncoherent uniform lattice in Isom(H4) was given by Bowditch and Mess [4]. In what follows we will identify Hn with a connected component of the hyperboloid {x : f (x) = −1} ⊂ Rn+1,