Let X be an infinite, connected, locally finite and vertex-transitive graph with infinitely many ends and let G be a subgroup of Aut(X) which acts transitively on X. In this note we provide a necessary and sufficient condition for the existence of a hyperbolic translation g in G with fixed ends in two prescribed open subsets ofthe space of ends of X. We also give an explicit combinatorial construction of the hyperbolic translation g in the special casewhere X is a (right) Cayley graph of a (non-abelian) free group of finite type G.
|Numero di pagine||10|
|Rivista||BOLLETTINO DI MATEMATICA PURA E APPLICATA|
|Stato di pubblicazione||Published - 2009|