Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems
نویسندگان
چکیده
منابع مشابه
Relatively hyperbolic groups: Intrinsic geometry, algebraic properties, and algorithmic problems
Open questions 100 1 Appendix. Equivalent definitions of relative hyperbolicity 103 Bibliography 108 2 Chapter 1 Introduction 1.1 Preliminary remarks Originally, the notion of a relatively hyperbolic group was proposed by Gromov [45] in order to generalize various examples of algebraic and geometric nature such as fundamental groups of finite–volume non–compact Riemannian mani-folds of pinched ...
متن کاملAlgorithmic Properties of Relatively Hyperbolic Groups
The following discourse is inspired by the works on hyperbolic groups of Epstein, and Neumann/Reeves. In [E], it is shown that geometrically finite hyperbolic groups are biautomatic. In [NR1], it is shown that virtually central extensions of word hyperbolic groups are biautomatic. We prove the following generalisation: Theorem 1. Let H be a geometrically finite hyperbolic group. Let σ ∈ H(H) an...
متن کاملBounded geometry in relatively hyperbolic groups
If a group is relatively hyperbolic, the parabolic subgroups are virtually nilpotent if and only if there exists a hyperbolic space with bounded geometry on which it acts geometrically finitely. This provides, via the embedding theorem of M. Bonk and O. Schramm, a very short proof of the finiteness of asymptotic dimension for such groups (which is known to imply Novikov conjectures).
متن کاملRelatively hyperbolic groups: geometry and quasi-isometric invariance
In this paper it is proved that relative hyperbolicity is an invariant of quasi-isometry. As a byproduct we provide simplified definitions of relative hyperbolicity in terms of the geometry of a Cayley graph. In particular we obtain a definition very similar to the one of hyperbolicity, relying on the existence for every quasi-geodesic triangle of a central left coset of peripheral subgroup.
متن کاملRelatively hyperbolic Groups
In this paper we develop some of the foundations of the theory of relatively hyperbolic groups as originally formulated by Gromov. We prove the equivalence of two definitions of this notion. One is essentially that of a group admitting a properly discontinuous geometrically finite action on a proper hyperbolic space, that is, such that every limit point is either a conical limit point or a boun...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2006
ISSN: 0065-9266,1947-6221
DOI: 10.1090/memo/0843