[en] Carrier graphs were first introduced for closed hyperbolic 3-manifolds
by White. In this paper, we first generalize this definition to carrier graphs for
representations of a rank two free group into the isometry group of hyperbolic
three space. Then we prove the existence and the finiteness of minimal carrier
graphs for those representations which are discrete, faithful and geometrically
finite, and more generally, those that satisfy certain finiteness conditions first
introduced by Bowditch.
Disciplines :
Mathematics
Author, co-author :
Tan, Ser Peow; National University of Singapore > Mathematics
XU, Binbin ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
CARRIER GRAPHS FOR REPRESENTATIONS OF THE RANK TWO FREE GROUP INTO ISOMETRIES OF HYPERBOLIC THREE SPACE
