共查询到20条相似文献,搜索用时 15 毫秒
1.
Richard Chow 《Transactions of the American Mathematical Society》1996,348(5):1757-1769
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.
2.
We consider discrete, faithful, type-preserving representations of the fundamental group of a punctured Riemann surface into PU(21), the holomorphic isometry group of complex hyperbolic space. Our main result is that there is a continuous family of such representations which interpolates between -Fuchsian representations and -Fuchsian representations. Moreover, these representations take every possible (real) value of the Toledo invariant. This contrasts with the case of closed surfaces where -Fuchsian and -Fuchsian representations lie in different components of the representation variety. In that case the Toledo invariant lies in a discrete set and indexes the components of the representation variety. 相似文献
3.
本文第一部分对组台群论的发展史作了一个简要的回顾.然后重点介绍近20年来组合群论领域中的三个热点课题:即双曲群,自动机群和群的Dehn函数的有关概念,并对相关的重要研究成果给予概述,其中包括作者本人在群的二阶Dehn函数的研究工作中的若干成果.最后提出9个公开问题。 相似文献
4.
We prove that certain hyperbolic Coxeter groups are separable on their geometrically finite subgroups. 相似文献
5.
A group G is called an A-group, where A is a given Abelian group, if it comes equipped with an action of A on G which mimics the way in which Z acts on any group. This action is codified in terms of certain axioms, all but one of which were introduced some years ago by R. C. Lyndon. For every such G and A there exists an A-exponential group G
A
which is the A-completion of G. We prove here that if G is a torsion-free hyperbolic group and if A is a torsion-free Abelian group, then the Lyndon's type completion G
A
of G is G-discriminated by G. This implies various model-theoretic and algorithmic results about G
A
. 相似文献
6.
Paul Schmutz Schaller 《Compositio Mathematica》2000,122(3):243-260
Let M be a hyperbolic surface and (M) its extended mapping class group. We show that (M) is isomorphic to the automorphism group of the following graph G(M). The set of vertices of G(M) is the set S(M) of nonseparating simple closed geodesics of M. Two vertices u and v of S(M) are related by an edge if u and v intersect exactly once in M. The graph G(M) can be thought of as a combinatorial model for M. 相似文献
7.
D. V. Osin 《Functional Analysis and Its Applications》2002,36(4):290-297
Let H be an infinite hyperbolic group with Kazhdan property (T) and let (H,X) denote the Kazhdan constant of H with respect to a generating set X. We prove that infX(H,X)=0, where the infimum is taken over all finite generating sets of H. In particular, this gives an answer to a Lubotzky question. 相似文献
8.
The structure of the space of orbits of PU(n, 1) acting on (n+1)-tuples of points in complex hyperbolic space is characterized in terms of side lengths and angular invariants. The more general situation in which some of the points lie on the boundary of complex hyperbolic space is described in terms of other basic invariants. 相似文献
9.
On the Isometry Groups of Hyperbolic Orbifolds 总被引:1,自引:0,他引:1
John G. Ratcliffe 《Geometriae Dedicata》1999,78(1):63-67
A generic, geometrically finite, hyperbolic n-orbifold is proved to have a finite group of isometries. 相似文献
10.
We use the complex and quaternionic hyperbolic versions of Jørgensen's inequality to construct embedded collars about short, simple, closed geodesics in complex and quaternionic hyperbolic manifolds. In general, the width of these collars depend both on the length of the geodesic and on the rotational part of the group element uniformising it. For complex hyperbolic space we are able to use a lemma of Zagier to give an estimate based only on the length. We show that these canonical collars are disjoint from each other and from canonical cusps. We also calculate the volumes of these collars. 相似文献
11.
Victor Gerasimov 《Geometric And Functional Analysis》2009,19(1):137-169
Let a discrete group G act by homeomorphisms of a compactum in a way that the action is properly discontinuous on triples and cocompact on pairs.
We prove that such an action is geometrically finite. The converse statement was proved by P. Tukia [T3]. So, we have another
topological characterisation of geometrically finite convergence groups and, by the result of A. Yaman [Y2], of relatively
hyperbolic groups. Further, if G is finitely generated then the parabolic subgroups are finitely generated and undistorted. This answer to a question of B.
Bowditch and eliminates restrictions in some known theorems about relatively hyperbolic groups.
Received: April 2007, Revision: May 2008, Accepted: August 2008 相似文献
12.
Let M be a hyperbolic three-manifold which is an n-fold cyclic branched covering of a hyperbolic link L in the three-sphere, or more precisely, of the hyperbolic three-orbifold
whose underlying topological space is the three-sphere and whose singular set, of branching index n, the link L. We say that M has no hidden symmetries (with respect to the given branched covering) if the isometry group of M is the lift of (a subgroup of) the isometry group of the hyperbolic orbifold
(which is isomorphic to the symmetry group of the link L). It follows from Thurston's hyperbolic surgery theorem that M has no hidden symmetries if n is sufficiently large. Our main result is an explicit numerical version of this fact: we give a constant, in terms of the volume of the complement of L, such that M has no hidden symmetries for all n larger than this constant; we show by examples that a universal constant working for all hyperbolic knots or links does not exist. We give also some results on the possible orders and the structure of the isometry group of M. Finally, we construct sets of four different -hyperbolic knots which have the same two-fold branched covering (a hyperbolic three-manifold); it is an interesting question for how many different -hyperbolic knots (or links) this may happen (in the case of hyperbolic knots, for arbitrarily many). 相似文献
13.
Jørgensen's inequality gives a necessary condition for a nonelementary two generator group of isometries of hyperbolic space to be discrete. We give analogues of Jørgensen's inequality for nonelementary groups of isometries of complex hyperbolic 2-space generated by two elements, one of which is either loxodromic or boundary elliptic. These results give an improvement over earlier results of Basmajian and Miner. 相似文献
14.
J. Tölke 《Geometriae Dedicata》2001,84(1-3):35-39
We prove a hyperbolic analogon of the euclidean theorem of Abramescu. The proof makes use of the basic concepts of plane hyperbolic differential geometry of G. W. M. Kallenberg. 相似文献
15.
Andrzej Szczepański 《Geometriae Dedicata》2002,93(1):139-142
We present a new class of examples of relatively hyperbolic groups in the weak sense. We use the construction of relative hyperbolization of polyhedra the idea of which comes from M. Gromov but technically was elaborated by R. Charney, M. Davis and T. Januszkiewicz. 相似文献
16.
According to the planar version of Ivory's theorem, the family of confocal conics has the property that in each curvilinear quadrangle formed by two pairs of conics the diagonals are of equal length. It turned out that this theorem is closely related to selfadjoint affine transformations. This point of view opens up a possibility of generalizing the Ivory theorem to the hyperbolic and other spaces. 相似文献
17.
Victor Pambuccian 《Mathematical Logic Quarterly》2001,47(4):475-488
We provide a universal axiom system for plane hyperbolic geometry in a firstorder language with two sorts of individual variables, ‘points’ (upper‐case) and ‘lines’ (lowercase), containing three individual constants, A0, A1, A2, standing for three non‐collinear points, two binary operation symbols, φ and ι, with φ(A, B) = l to be interpreted as ‘𝓁 is the line joining A and B’ (provided that A ≠ B, an arbitrary line, otherwise), and ι(g, h) = P to be interpreted as 𝓁P is the point of intersection of g and h (provided that g and h are distinct and have a point of intersection, an arbitrary point, otherwise), and two binary operation symbols, π1(P, 𝓁) and —2(P, 𝓁), with πi(P, 𝓁) = g (for i = 1, 2) to be interpreted as ‘g is one of the two limiting paralle lines from P to 𝓁 (provided that P is not on 𝓁, an arbitrary line, otherwise). 相似文献
18.
Florence Newberger 《Geometriae Dedicata》2003,97(1):215-249
The goal of this paper is to provide a tool, the Global Measure Formula, that will facilitate the study of the limit set of discrete geometrically finite groups of isometries of the rank one symmetric spaces. We consider the shadow of a ball from a fixed reference point onto the boundary, and prove a formula that describes the measure of the shadow in terms of the center of the shadowed ball, generalizing a result from real hyperbolic geometry. 相似文献
19.
Po-Hsun Hsieh 《Geometriae Dedicata》2003,97(1):93-98
Two bisectors in complex hyperbolic space H
n are called cotranchal if they possess a common slice. We define a natural thing called the prespinal angle between two such bisectors and use it to study the intersection of two such bisectors. 相似文献
20.
Let Heis
2n+1 be the Heisenberg group of dimension 2n + 1 and M an infra-nilmanifold with Heis
2n+1-geometry. The fundamental group of M contains a cocompact lattice of Heis
2n+1 with index bounded above by a universal constant I
n+1, i.e., I
n+1 is the maximal order of the holonomy groups. We prove that I
3 = 24. As an application we give an estimate for the volumes of finite volume non-compact complex hyperbolic 3-manifolds. 相似文献