This paper is the first in a sequence on the structure of sets of solutions to systems of
equations in a free group, projections of such sets, and the structure of elementary sets …

The theory of?-trees has its origin in the work of Lyndon on length functions in groups. The
first definition of an R-tree was given by Tits in 1977. The importance of?-trees was …

A Leitmotiv of geometric group theory is the study of group actions on geometric structures,
from which one can draw conclusions about both the group and the geometry. A typical and …

We introduce a combinatorial version of Stallings–Bestvina–Feighn–Dunwoody folding
sequences. We then show how they are useful in analyzing the solvability of the uniform …

Using the canonical JSJ decomposition [9, 12] we prove that every torsion-free hyperbolic
group is Hopf. This implies, in particular, that if M and N are closed negatively curved …

This survey is intended to be a fast (and reasonably updated) reference for the theory of
Stallings automata and its applications to the study of subgroups of the free group, with the …

We define the notion of a “peripheral splitting” of a group. This is essentially a representation
of the group as the fundamental group of a bipartite graph of groups, where all the vertex …

Makanin–Razborov diagrams for hyperbolic groups Page 1 ANNALES MATHÉMATIQUES
BLAISE PASCAL RW & CR Makanin–Razborov diagrams for hyperbolic groups Volume 26 …

Bestvina and Feighn showed that a morphism S→ T between two simplicial trees that
commutes with the action of a group G can be written as a product of elementary folding …

We study an abstract notion of tree structure which lies at the common core of various tree-
like discrete structures commonly used in combinatorics: trees in graphs, order trees, nested …