The Grushko decomposition of a finite graph of finite rank free groups: an algorithm.
The Homotype Type of a Combinatorially Aspherical Presentation.
The th root of a braid is unique up to conjugacy.
The number of sides of a parallelogram.
The rank of actions on -trees
The rate of escape for random walks on polycyclic and metabelian groups
We use subgroup distortion to determine the rate of escape of a simple random walk on a class of polycyclic groups, and we show that the rate of escape is invariant under changes of generating set for these groups. For metabelian groups, we define a stronger form of subgroup distortion which applies to non-finitely generated subgroups. Under this hypothesis, we compute the rate of escape for certain random walks on some abelian-by-cyclic groups via a comparison to the toppling of a dissipative abelian...
The rhombic dodecahedron and semisimple actions of Aut(Fₙ) on CAT(0) spaces
We consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fₙ) has a fixed point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-generated ℤ⁴ ⊂ Aut(F₃) leaves invariant an isometrically embedded copy of Euclidean 3-space 𝔼³ ↪ X on which it acts as a discrete group of translations with the rhombic dodecahedron as a Dirichlet...
The shape of a group---connections between shape theory and the homology of groups
The square model for random groups
We introduce a new random group model called the square model: we quotient a free group on n generators by a random set of relations, each of which is a reduced word of length 4. We prove that, just as in the Gromov model, for densities > 1/2 a random group in the square model is trivial with overwhelming probability and for densities < 1/2 a random group is hyperbolic with overwhelming probability. Moreover, we show that for densities d < 1/3 a random group in the square model does not...
The symmetry of intersection numbers in group theory.
The tame automorphism group of an affine quadric threefold acting on a square complex
We study the group of tame automorphisms of a smooth affine -dimensional quadric, which we can view as the underlying variety of . We construct a square complex on which the group admits a natural cocompact action, and we prove that the complex is and hyperbolic. We propose two applications of this construction: We show that any finite subgroup in is linearizable, and that satisfies the Tits alternative.
Thompson's group is not minimally almost convex.
Three amalgams of A_5
Topological dimensions for -groups.
Torsion Free Subgroups of Fuchsian Groups and Tessalations of Surfaces.
Towards the Hanna Neumann conjecture using Dicks's method.
Trees of manifolds and boundaries of systolic groups
We prove that the Pontryagin sphere and the Pontryagin nonorientable surface occur as the Gromov boundary of a 7-systolic group acting geometrically on a 7-systolic normal pseudomanifold of dimension 3.
Trees of manifolds with boundary
We introduce two new classes of compacta, called trees of manifolds with boundary and boundary trees of manifolds with boundary. We establish their basic properties.
Trees, valuations, and the Bieri-Neumann-Strebel invariant.
Undirected and directed graphs with near polynomial growth
The growth function of a graph with respect to a vertex is near polynomial if there exists a polynomial bounding it above for infinitely many positive integers. In the paper vertex-symmetric undirected graphs and vertex-symmetric directed graphs with coinciding in- and out-degrees are described in the case their growth functions are near polynomial.