An infinitely generated intersection of geometrically finite hyperbolic groups

Abstract

Two discrete, geometrically finite subgroups of the isometries of hyperbolic n-space ( n ≥ 4 n \ge 4 ) are defined whose intersection is infinitely generated. This settles, in dimensions 4 and above, a long-standing question in Kleinian and hyperbolic groups reiterated at a problem session chaired by Bernard Maskit at the AMS meeting 898, March 3–5, 1995, a conference in honor of Bernard Maskit’s 60th birthday.