Moduli of triples of points in quaternionic hyperbolic geometry

In this work, we describe the moduli of triples of points in quaternionicprojective space which define uniquely the congruence classes of such triplesrelative to the action of the isometry group of quaternionic hyperbolic space${\rm H}^n_{\mathbb{Q}}$. To solve this problem, we introduce some basicinvariants of triples of points in quaternionic hyperbolic geometry. Inparticular, we define quaternionic analogues of the Goldman invariants formixed configurations of points introduced by him in complex hyperbolicgeometry.