TY - JOUR

T1 - On the fixed ends of hyperbolic translations of infinite graphs

AU - Pavone, Marco

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

KW - Cayley graph

KW - Graph with infinitely many ends

KW - hyperbolic translation

KW - Cayley graph

KW - Graph with infinitely many ends

KW - hyperbolic translation

UR - http://hdl.handle.net/10447/61017

M3 - Article

VL - II

SP - 5

EP - 14

JO - BOLLETTINO DI MATEMATICA PURA E APPLICATA

JF - BOLLETTINO DI MATEMATICA PURA E APPLICATA

ER -