MA 335: Introduction to Hyperbolic Manifolds

Credits: 3:0

Prerequisite courses: MA 231

Pre-requisites :

1. Topology (MA 231)
2. 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:

1. Ratcliffe, Foundations of Hyperbolic Manifolds
2. Benedetti-Petronio, Lectures on Hyperbolic Geometry
3. Martelli, Introduction to Geometric Topology

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