A 1 1/2-dimensional version of Hopf's Theorem on the number of ends of a group.
A cyclically pinched product of free groups which is not residually free.
A Free Product with a Non-Power Amalgamated which is not Residually Free.
A generalized Hopf formula for higher homology groups.
A non-quasiconvex subgroup of a hyperbolic group with an exotic limit set.
A numerical invariant for finitely generated groups via actions on graphs.
A remark on the intersection of the conjugates of the base of quasi-HNN groups.
A Residual Property of Certain Free Products.
A short proof of a theorem of Brodskii.
A short proof, using graphs and groupoids, is given of Brodskii’s theorem that torsion-free one-relator groups are locally indicable.
A simple proof of Vinogradov’s theorem on the orderability of the free product of -groups
A spelling theorem for staggered generalized 2-complexes, with applications.
Abelian subgroup separability of some one-relator groups.
Actions de groupes sur les arbres
Actions of finitely generated groups on -trees
We study actions of finitely generated groups on -trees under some stability hypotheses. We prove that either the group splits over some controlled subgroup (fixing an arc in particular), or the action can be obtained by gluing together actions of simple types: actions on simplicial trees, actions on lines, and actions coming from measured foliations on -orbifolds. This extends results by Sela and Rips-Sela. However, their results are misstated, and we give a counterexample to their statements.The...
Active sums I.
Given a generating family F of subgroups of a group G closed under conjugation and with partial order compatible with inclusion, a new group S can be constructed, taking into account the multiplication in the subgroups and their mutual actions given by conjugation. The group S is called the active sum of F, has G as a homomorph and is such that S/Z(S) ≅ G/Z(G) where Z denotes the center.The basic question we investigate in this paper is: when is the active sum S of the family F isomorphic to the...
Active sums of groups.
Adjoining conjugating elements to finite groups
Algorithmic verification of quasi-isometry of some HNN-extensions of Abelian groups.
Almost all one-relator groups with at least three generators are residually finite
We prove that with probability tending to 1, a one-relator group with at least three generators and the relator of length is residually finite, is a virtually residually (finite -)group for all sufficiently large , and is coherent. The proof uses both combinatorial group theory and non-trivial results about Brownian motions.
Amalgamated products and finitely presented groups.