Regular geodesic languages and the falsification by fellow traveler property.
Regular neighbourhoods and canonical decompositions for groups.
Representations of a free group of rank two by time-varying Mealy automata
In the group theory various representations of free groups are used. A representation of a free group of rank two by the so-calledtime-varying Mealy automata over the changing alphabet is given. Two different constructions of such automata are presented.
Rigidity of graph products of groups.
R-trees and the Bieri-Neumann-Strebel invariant.
Let G be a finitely generated group. We give a new characterization of its Bieri-Neumann-Strebel invariant Σ(G), in terms of geometric abelian actions on R-trees. We provide a proof of Brown's characterization of Σ(G) by exceptional abelian actions of G, using geometric methods.