ORTHOGONAL COMPLEX HYPERBOLIC ARRANGEMENTS

IntroductionThe purpose of this note is to study the geometry of certain remarkable innitearrangements of hyperplanes in complex hyperbolic space which we call orthogonalarrangements : whenever two hyperplanes meet, they meet at right angles. Anatural example of such an arrangement appears in [3]; see also [2]. The concretetheorem that we prove here is that the fundamental group of the complement ofan orthogonal arrangement has a presentation of a certain sort. As an applicationof this ...