Gisele Teixeira Paula: Height estimates for Bianchi groups
Consider the geometry of the action of Bianchi groups SL(2,Od) on the hyperbolic space H3, where Od is the ring of integers of the imaginary quadratic field K=Q(√−d). We obtain, for some values of d, an upper estimate for the height of some matrix M that takes a given point (z,t)∈H3 into the fundamental domain of the Bianchi group. This generalizes a lemma of Habegger and Pila about the action of the modular group on H2. We use coarse fundamental domains that look like the so-called Siegel sets to make computations easier.
