Farey polytopes and continued fractions associated with discrete hyperbolic groups

Abstract

The known definitions of Farey polytopes and continued fractions are generalized and applied to diophantine approximation in n n -dimensional euclidean spaces. A generalized Remak-Rogers isolation theorem is proved and applied to show that certain Hurwitz constants for discrete groups acting in a hyperbolic space are isolated. The approximation constant for the imaginary quadratic field of discriminant − 15 -15 is found.