Related papers: Combination theorems for geometrically finite conv…

We state and prove a combination theorem for relatively hyperbolic groups seen as geometrically finite convergence groups. For that, we explain how to contruct a boundary for a group that is an acylindrical amalgamation of relatively…

We prove a combination theorem for hyperbolic groups, in the case of groups acting on complexes displaying combinatorial features reminiscent of non-positive curvature. Such complexes include for instance weakly systolic complexes and…

In this paper, we state two combination theorems for relatively quasiconvex subgroups in a relatively hyperbolic group. Applications are given to the separability of double cosets of certain relatively quasiconvex subgroups and the…

We prove the convex combination theorem for hyperbolic n-manifolds. Applications are given both in high dimensions and in 3 dimensions. One consequence is that given two geometrically finite subgroups of a discrete group of isometries of…

We provide sufficient conditions for two subgroups of a hierarchically hyperbolic group to generate an amalgamated free product over their intersection. The result applies in particular to certain geometric subgroups of mapping class groups…

The aim of this article is to give a survey of combination theorems occurring in hyperbolic geometry, geometric group theory and complex dynamics, with a particular focus on Thurston's contribution and influence in the field.

In this paper, we prove a limit set intersection theorem in relatively hyperbolic groups. Our approach is based on a study of dynamical quasiconvexity of relatively quasiconvex subgroups. Using dynamical quasiconvexity, many well-known…

We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and…

In this paper we prove a combination theorem for Veech subgroups of the mapping class group analogous to the first Klein-Maskit combination theorem for Kleinian groups in which two Fuchsian subgroups are amalgamated along a parabolic…

We prove a combination theorem for trees of (strongly) relatively hyperbolic spaces and finite graphs of (strongly) relatively hyperbolic groups. This gives a geometric extension of Bestvina and Feighn's Combination Theorem for hyperbolic…

The first author and Oguni introduced a class of groups of non-positive curvature, called coarsely convex group. The recent success of the theory of groups which are hyperbolic relative to a collection of subgroups has motivated the study…

Carrier graphs of groups representing subgroups of a given relatively hyperbolic groups are introduced and a combination theorem for relatively quasi-convex subgroups is proven. Subsequently a theory of folds for such carrier graphs is…

In this article, we prove a combination theorem for a complex of relatively hyperbolic groups. It is a generalization of Martin's \cite{martin} work for combination of hyperbolic groups over a finite $M_K$-simplicial complex, where $k\leq…

In this paper, we study the class of parabolically geometrically finite (PGF) subgroups of mapping class groups, introduced by Dowdall-Durham-Leininger-Sisto. We prove a combination theorem for graphs of PGF groups (and other…

The purpose of this paper is to consider some basic constructions in the category of compact quantum groups --for example de case of extensions, of Drinfeld twists, of matched pairs, of extensions, of linked pairs and of cocycle Singer…

This is an announcement of some of the results obtained as a part of the second author's Ph.D. thesis. In the first part, we prove that the fundamental group of an acylindrical complex of hyperbolic groups with finite edge groups is…

We prove a general combination theorem for discrete subgroups of $\mathrm{PGL}(n,\mathbb{R})$ preserving properly convex open subsets in the projective space $\mathbb{P}(\mathbb{R}^n)$, in the spirit of Klein and Maskit. We use it in…

We present examples of geometrically finite manifolds with pinched negative curvature, whose geodesic flow has infinite non-ergodic Bowen-Margulis measure and whose Poincar\'e series converges at the critical exponent $\delta_\Gamma$. We…

In this paper, we prove a combination theorem for a relatively acylindrical graph of relatively hyperbolic groups (Theorem 1.1). Here, we are extending the technique of [Tom21] and constructing Bowditch boundary of the fundamental group of…

In this paper, we generalise the first Klein-Maskit combination theorem to discrete groups of M\"{o}bius transformations in higher dimensions. As a simple application of the main theorem, some examples will be constructed.