Introduction to Algebraic Topology (MA 232) or equivalent.
This is an introduction to hyperbolic surfaces and 3-manifolds, which played a key role in the development of geometric topology in the preceding few decades.
Topics that shall be discussed will be from the following list:
Basic notions of Riemannian geometry, Models of hyperbolic space, Fuchsian groups, Thick-thin decomposition, Teichmüller space, The Nielsen Realisation problem, Kleinian groups, The boundary at infinity, Mostow rigidity theorem, 3-manifold topology and the JSJ-decomposition, Statement of Thurston’s Geometrization Conjecture (proved by Perelman)
Suggested books and references:
Ratcliffe, Foundations of Hyperbolic Manifolds.
Benedetti-Petronio, Lectures on Hyperbolic Geometry.