4 papers · 1 filter
Foldings, graphs of groups and the membership problem
Ilya Kapovich, Richard Weidmann, Alexei Myasnikov
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…
Acylindrical accessibility for groups acting on -trees
Ilya Kapovich, Richard Weidmann
We prove an acylindrical accessibility theorem for finitely generated groups acting on -trees. Namely, we show that if is a freely indecomposable non-cyclic -gene…
Nielsen methods and groups acting on hyperbolic spaces
Ilya Kapovich, Richard Weidmann
We show that for any positive integer there exists a constant such that any -generated group , which acts by isometries on a -hyperbolic space (with ), i…
Freely indecomposable groups acting on hyperbolic spaces
Ilya Kapovich, Richard Weidmann
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 fini…