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Sunday, July 12, 2020 | History

4 edition of Relatively hyperbolic groups found in the catalog.

Relatively hyperbolic groups

intrinsic geometry, algebraic properties, and algorithmic problems

by Denis V. Osin

  • 36 Want to read
  • 4 Currently reading

Published by American Mathematical Society in Providence, R.I .
Written in English

    Subjects:
  • Geometric group theory.,
  • Hyperbolic groups.

  • Edition Notes

    StatementDenis V. Osin.
    SeriesMemoirs of the American Mathematical Society,, no. 843
    Classifications
    LC ClassificationsQA3 .A57 no. 843, QA183 .A57 no. 843
    The Physical Object
    Paginationp. cm.
    ID Numbers
    Open LibraryOL3428957M
    ISBN 100821838210
    LC Control Number2005053663

    ISRAEL JOURNAL OF MATHEMATICS (), { DOI: /s DEHN FILLING IN RELATIVELY HYPERBOLIC GROUPS BY Daniel Groves⁄,y California Institute of Technol. I have two questions about relatively hyperbolic groups. They sound elementary, but I haven't seen an explicit answer in, for example, papers by Farb or Bowditch. Is a free product of finitely many relatively hyperbolic groups itself relatively hyperbolic (relative to the collection of given parabolic subgroups)?

    We introduce the bounded packing property for a subgroup of a countable discrete group G. This property gives a finite upper bound on the number of left cosets of the subgroup that are pairwise close in G. We establish basic properties of bounded packing, and give many examples; for instance, every subgroup of a countable, virtually nilpotent group has bounded packing. We explain several. Gromov's hyperbolic groups has been published in , probably written in Both other books have been published in , so these rather provide the state of .

    Using the definition of Farb of a relatively hyperbolic group in the strong sense [B Farb, Relatively hyperbolic groups, Geom. Func. Anal. 8 () ], we prove this assertion. Vertex niteness for splittings of relatively hyperbolic groups Vincent Guirardel and Gilbert Levitt Septem Abstract Consider a group Gand a family Aof subgroups of G. We say that vertex niteness holds for splittings of Gover Aif, up to isomorphism, there are only nitely many.


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Relatively hyperbolic groups by Denis V. Osin Download PDF EPUB FB2

In this paper we obtain an isoperimetric characterization of relatively hyperbolicity of a groups with respect to a collection of subgroups. This allows us to apply classical combinatorial methods related to van Kampen diagrams to obtain relative analogues of some well–known algebraic and geometric properties of ordinary hyperbolic groups.

Destination page number Search scope Search Text. Relatively Hyperbolic Groups. Farb 1 Hyperbolic Group; Access options Buy single article.

Instant access to the full article PDF. US$ Price includes VAT for USA. Rent this article via DeepDyve. Learn more about Institutional subscriptions. by: The main aim of this paper is to give an account of the notion of a “relatively hyper- bolic group”, or more precisely, a group which is “hyperbolic relative to” a preferred class of “peripheral subgroups”.

This is very general notion which encompasses a wide class of naturally Relatively hyperbolic groups book groups. Abstract. 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 bounded parabolic by: Such a larger class of groups is called relatively hyperbolic groups.

An element gof is called parabolic if it lies in a conjugate of some parabolic subgroup H i; otherwise, the element gis called hyperbolic. In the same paper [Gro87], Gromov introduced the notion of a relatively hyperbolic group as a generalization of a hyperbolic group.

Polynomial growth for groups and bounded geometry for horoballs 92 3. Proof of Theorem 93 References 94 The class of relatively hyperbolic groups is an important class of groups en-compassing hyperbolic groups, fundamental groups of geometrically finite orbifolds with pinched negative curvature, groups acting on CAT(0) spaces with isolated.

LIMIT GROUPS FOR RELATIVELY HYPERBOLIC GROUPS, I: THE BASIC TOOLS. DANIEL GROVES Abstract. We begin the investigation of -limit groups, where is a torsion-free group which is hyperbolic relative to a collection of free abelian subgroups.

Using the results of [16], we adapt the results from [22]. Speci cally, given a nitely generated group G. Intuitive definition. A group G is relatively hyperbolic with respect to a subgroup H if, after contracting the Cayley graph of G along H-cosets, the resulting graph equipped with the usual graph metric becomes a δ-hyperbolic space and, moreover, it satisfies a technical condition which implies that quasi-geodesics with common endpoints travel through approximately the same collection of.

group with infinitely many ends, then G splits as a graph of groups with finite edge–groups. In this book we provide two proofs of the above theorem, which, while quite.

Small cancellations over relatively hyperbolic groups and embedding theorems. Pages from Volume (), Issue 1 by Denis Osin. Relatively hyperbolic groups are a class generalising hyperbolic groups.

Very roughly is hyperbolic relative to a collection of subgroups if it admits a (not necessarily cocompact) properly discontinuous action on a proper hyperbolic space which is "nice" on the boundary of and such that the stabilisers in of points on the boundary are.

Abstract: Given a probability measure on a finitely generated group, its Martin boundary is a way to compactify the group using the Green's function of the corresponding random walk.

We give a complete topological characterization of the Martin boundary of finitely supported random walks on relatively hyperbolic groups with virtually abelian parabolic subgroups.

Keywords: Relatively hyperbolic groups; SQ-universality 1. Introduction The notion of a group hyperbolic relative to a collection of subgroups was originally sug-gested by Gromov [9] and since then it has been elaborated from different points of view [3,5, 6,20].

The class of relatively hyperbolic groups includes many examples. For instance, if. We follow the approach to relatively hyperbolicity given by Osin [Os_book]. Say G is a finitely generated group that is relatively hyperbolic with respect to a family of subgroups { H i }.

‘p-spaces for relatively hyperbolic groups 39 saythat] c(x 1,x 2) 6θotherwise,namely,ifforanygeodesicbetweencandx i and startingbyandedgee i(i= 1,2),then] c(e 1,e. Relatively hyperbolic groups were first defined by Gromov in his seminal paper on hyperbolic groups [16, Subsectionp].

Another definition was given by Farb [15, Section 3], and further definitions given by Bowditch [7, Definitions 1 and 2, page 1]. Relatively hyperbolic groups: intrinsic geometry, algebraic properties, and algorithmic problems. [Denis V Osin] This book allows us to apply classical combinatorial methods related to Read more Rating: (not yet rated) 0 with reviews - Be the first.

Subjects: Geometric group theory. Hyperbolic groups. theory of groups. From various points of view, the notion of relative hyperbolicity has been considered by many authors, cf.

[12], [2], [16], [6], and [9], just to name a few. These theories of relatively hyperbolic groups emphasize different aspects and are widely accepted to be equivalent for finitely generated groups. tation of a hyperbolic group, computes the number of ends of the group.

In this paper, we consider relatively hyperbolic groups. (See Section 2 for a definition.) Following Gerasimov's ideas, our main result is: Theorem There exists an algorithm which takes as input a finite presentation of a group T which is hyperbolic relative to abelian.

relatively hyperbolic groups. uction Many properties of hyperbolic groups seem natural to extend to relatively hyperbolic groups. A group is hyperbolic if it acts properly and cocompactly on a hyperbolic space. Roughly speaking, a group is hyperbolic relative to a subgroup if, modulo that subgroup, it acts properly on a hyperbolic space.QUASI-HYPERBOLIC PLANES IN RELATIVELY HYPERBOLIC GROUPS andAlessandroSisto UniversityofBristol,SchoolofMathematics Bristol,UnitedKingdom;@ ETHZurich,DepartmentofMathematics Zurich,Switzerland;[email protected] Abstract.

We show that any group that is hyperbolic .Examples include relatively hyperbolic groups, acylindrical groups, WPD groups and weakly hyperbolic groups.

The goal of this workshop is to bring together people with expertise in geometric group theory, ergodic theory, probability and related areas to develop the theory of random walks on groups of isometries of hyperbolic spaces and other.