Finitely presentable, non-Hopfian groups with Kazhdan's Property (T) and infinite outer automorphism group

Endomorphisms of relatively hyperbolic groups

We generalize some results of Paulin and Rips-Sela on endomorphisms of hyperbolic groups to relatively hyperbolic groups, and in particular prove the following. (1) If G is a finitely generated non-elementary relatively hyperbolic group with slender parabolic subgroups, and either G is not co-Hopfian or Out(G) is infinite, then G splits over a slender group. (2) If a finitely generated non-parabolic subgroup H of a non-elementary relatively hyperbolic group is not Hopfian, then H acts non-trivially on an R-tree. (3) Every non-elementary relatively hyperbolic group has a non-elementary relative…

关于有限生成单左序群$G_ρ$的一些代数与解析性质

On some algebraic and analytic properties of the finitely generated simple left orderable groups $G_ρ$

本文研究了Hyde与第二作者构造的首个有限生成单左序群族$G_ρ$，证明了其非有限可表示、非内顺从、无Kazhdan性质$(T)$但具性质FA、首$l^2$-Betti数为零，且为一致单群，并描述了周期标号下的群结构。

Groups of piecewise linear homeomorphisms of flows

To every dynamical system $(X,φ)$ over a totally disconnected compact space, we associate a left-orderable group $T(φ)$. It is defined as a group of homeomorphisms of the suspension of $(X,φ)$ which preserve every orbit of the suspension flow and act by dyadic piecewise linear homeomorphisms in the flow direction. We show that if the system is minimal, the group is simple, and if it is a subshift then the group is finitely generated. The proofs of these two statements are short and elementary, providing straightforward examples of finitely generated simple left-orderable groups. We show that i…