A continuation of the study of spherical, Euclidean and especially hyperbolic geometry in two and three dimensions. The emphasis will be on the relationship with topology, and the existence of metrics of constant curvature on a vast class of two and three dimensional manifolds.
We will concentrate mainly on a detailed study of examples, and we will try to be as explicit and as elementary as possible. Topics to be covered might include: uniformization for surfaces, shapes and volumes of hyperbolic polyhedra, circle packing and Andreev's theorem, and hyperbolic structures on knot complements. |