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 -