论文标题
双曲线组的亚组，有限性能和复杂的双曲线晶格
Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices
论文作者
论文摘要
我们证明，在共同的复杂双曲线算术晶格中$γ<{\ rm pu}（m，1）$的最简单类型的$，足够深的有限索引子组接受大量同构为$ \ mathbb {z} $ a f type $ \ nathscr {z} $ type $ \ mathscr {z} $ $ \ mathscr {f} _ {m} $。这提供了许多有限的双曲线组的非纤维化亚组，并回答了布雷迪的一个古老问题。我们的方法还提供了一种特殊情况，即辛格对非球体kähler歧管的猜想。
We prove that in a cocompact complex hyperbolic arithmetic lattice $Γ< {\rm PU}(m,1)$ of the simplest type, deep enough finite index subgroups admit plenty of homomorphisms to $\mathbb{Z}$ with kernel of type $\mathscr{F}_{m-1}$ but not of type $\mathscr{F}_{m}$. This provides many finitely presented non-hyperbolic subgroups of hyperbolic groups and answers an old question of Brady. Our method also yields a proof of a special case of Singer's conjecture for aspherical Kähler manifolds.
