Richard Weidmann

FOLDINGS, GRAPHS OF GROUPS AND THE MEMBERSHIP PROBLEM

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 subgroup membership problem for fundamental groups of graphs of groups. Applications include coherent right-angled Artin groups and coherent solvable groups.

Destabilizing amalgamated Heegaard splittings

Author(s): Schultens, Jennifer; Weidmann, Richard | Abstract: We construct a sequence of pairs of 3-manifolds each with torus boundary and with the following two properties: 1) For the result of a carefully chosen glueing of the nth pair of 3-manifolds along their boundary tori, the ratio of the genus of the resulting 3-manifold to the sum of the genera of the pair of 3-manifolds is less than 1/2. 2) The result of amalgamating certain unstabilized Heegaard splittings of the pair of 3-manifolds to form a Heegaard splitting of the resulting 3-manifold produces a stabilized Heegaard splitting that can be destabilized successively n times.

FREELY INDECOMPOSABLE GROUPS ACTING ON HYPERBOLIC SPACES

We obtain a number of finiteness results for groups acting on Gromov-hyperbolic spaces. In particular we show that a torsion-free locally quasiconvex hyperbolic group has only finitely many conjugacy classes of n-generated one-ended subgroups.

On the structure of two-generated hyperbolic groups

Abstract. We show that every two-generated torsion-free one-ended word-hyperbolic group has virtually cyclic outer automorphism group. This is done by computing the JSJ-decomposition for two-generator hyperbolic groups. We further prove that two-generated torsion-free word-hyperbolic groups are strongly accessible. This means that they can be constructed from groups with no nontrivial cyclic splittings by applying finitely many free products with amalgamation and HNN-extensions over cyclic subgroups.

Nielsen Methods and Groups Acting on Hyperbolic Spaces

We show that for any n & in ℕ there exists a constant C(n) such that any n-generated group G which acts by isometries on a δ-hyperbolic space (with δ>0) is either free or has a nontrivial element with translation length at most δC(n).

Two-generated groups acting on trees

Abstract. We study 2-generated subgroups of groups that act on simplicial trees. We show that any generating pair

Kleinian groups and the rank problem

\{{g},h\}

On the uniqueness of factors of amalgamated products

of such a subgroup is Nielsen-equivalent to a pair

Meridional rank and bridge number for a class of links

\{f,s\}

On invertible generating pairs of fundamental groups of graph manifolds

where either powers of f and s or powers of f and