A geometric proof that SL_2(Z[t,t^-1]) is not finitely presented

We give a new proof of the theorem of Krstic-McCool from the title. Our proof has potential applications to the study of finiteness properties of other subgroups of SL_2 resulting from rings of functions on curves.Comment: This is the version published by Algebraic & Geometric Topology on 11 July 200

From local to global conjugacy of subgroups of relatively hyperbolic groups

Suppose that a finitely generated group $G$ is hyperbolic relative to a collection of subgroups $\mathbb{P}=\{P_1,\dots,P_m\}$. Let $H_1,H_2$ be subgroups of $G$ such that $H_1$ is relatively quasiconvex with respect to $\mathbb{P}$ and $H_2$ is not parabolic. Suppose that $H_2$ is elementwise conjugate into $H_1$. Then there exists a finite index subgroup of $H_2$ which is conjugate into $H_1$. The minimal length of the conjugator can be estimated. In the case where $G$ is a limit group, it is sufficient to assume only that $H_1$ is a finitely generated and $H_2$ is an arbitrary subgroup of $G$.Comment: 14 pages, 1 Figure. The proof in this version is shorte