We consider a cocompact discrete reflection group W of a CAT(0) space X . Then W becomes a Coxeter group. In this paper, we study an analogy between the Davis-Moussong complex Σ(W, S) and the CAT(0) space X , and show several analogous results about the limit set of a parabolic subgroup of the Coxeter group W .

In this note, we prove that an aspherical fully residually free Kähler group is Fuchsian. One instances of this shows that cocompact lattices in PU(1, n) for n > 1 cannot be residually free. The proof uses some recent work of Delzant and Gromov.

A connection between real poles of the growth functions for Coxeter groups acting on hyperbolic space of dimensions three and greater and algebraic integers is investigated. In particular, a certain geometric convergence of fundamental domains for cocompact hyperbolic Coxeter groups with finite-volume limiting polyhedron provides a relation between Salem numbers and Pisot numbers. Several examp...

Let G be a complete Kac–Moody group of rank n ≥ 2 such that the Weyl group of G is a free product of cyclic groups of order 2. We construct new families of examples of cocompact lattices in G, many of which act transitively on the chambers of the building for G.

Let Γ be a cocompact Fuchsian group. We calculate the lower algebraic K-theory of the integral group ring ZΓ and find an explicit formula for Ki(ZΓ), i ≤ 1, in terms of the lower K-groups of finite cyclic groups.

We compute the Selberg trace formula for Hecke operators (also called the trace formula for modular correspondences) in the context of cocompact Kleinian groups with finite-dimentional unitary representations. We give some applications to the distribution of Hecke eigenvalues, and give an analogue of Huber’s theorem.

‎We determine the‎ ‎form of polynomially bounded solutions to the Loewner differential ‎equation that is satisfied by univalent subordination chains of the‎ ‎form $f(z,t)=e^{int_0^t A(tau){rm d}tau}z+cdots$‎, ‎where‎ ‎$A:[0,infty]rightarrow L(mathbb{C}^n,mathbb{C}^n)$ is a locally‎ ‎Lebesgue integrable mapping and satisfying the condition‎ ‎$$sup_{sgeq0}int_0^inftyleft|expleft{int_s^t‎ ‎[A(tau)...

let a be a banach algebra and e be a banach a-bimodule then s = a  e, the l1-direct sum of a and e becomes a module extension banach algebra when equipped with the algebras product (a; x):(a′; x′) = (aa′; a:x′ + x:a′). in this paper, we investigate △-amenability for these banach algebras and we show that for discrete inverse semigroup s with the set of idempotents es, the module extension bana...

let $r$ be a commutative ring with identity and $m$ be a finitely generated unital $r$-module. in this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. moreover, we investigate some conditions which imply that the module $m$ is the direct sum of some cyclic modules and free modules. then some properties of fitting ideals of...