We show that any finitely generated group quasi-isometric to complex hyperbolic space is a finite extension of a properly discontinuous, cocompact subgroup of the isometry group.

This paper is about geometric and topological properties of a proper CAT(0) spaceX which is cocompact i.e. which has a compact generating domain with respect to the full isometry group. It is shown that geodesic segments in X can “almost” be extended to geodesic rays. A basic ingredient of the proof of this geometric statement is the topological theorem that there is a top dimension d in which ...

We will say that a smooth projective complex algebraic variety V (of dimension n − 1) is a fake Pn−1 if V is the quotient of the unit ball Bn−1 by a torsion-free cocompact discrete subgroup of PU(n − 1, 1), and all the Betti numbers of V are equal to those of Pn−1 C . If the fundamental goup of a fake P n−1 is an arithmetic subgroup of PU(n − 1, 1), then we will say that it is an arithmetic fak...

Abstract The cusped hyperbolic n -orbifolds of minimal volume are well known for $n\leq 9$ . Their fundamental groups related to the Coxeter -simplex $\Gamma _{n}$ In this work, we prove that has growth rate among all non-cocompact finite covolume in $\textrm{Isom}\mathbb H^{n}$ way, extend previous results Floyd $n=2$ and Kellerhals $n=3$ , respectively. Our proof is a generalization methods d...

We give a superconnection proof of Connes’ index theorem for proper cocompact actions of étale groupoids. This includes Connes’ general foliation index theorem for foliations with Hausdor¤ holonomy groupoid.

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

Among other results, we rationally calculate the algebraic K-theory of any discrete cocompact subgroup of a Lie group G, where G is either O(n, 1), U(n, 1), Sp(n, 1), or F(4), in terms of the homology of the double coset space Gamma\G/K, where K is a maximal cocompact subgroup of G. We obtain the formula K(n)(ZGamma) [unk] [unk] congruent with [unk](i=0) (infinity)H(i)(Gamma\G/K; [unk](n-i)), w...