MATH 6640

Hyperbolic Geometry

Course Description

Course information provided by the Courses of Study 2023-2024.

An introduction to the topology and geometry of hyperbolic manifolds. The class will begin with the geometry of hyperbolic n-space, including the upper half-space, Poincaré disc, Klein, and Lorentzian models. We will cover both synthetic and computational approaches. We will then discuss hyperbolic structures on surfaces and 3-manifolds, and the corresponding groups of isometries (i.e. Fuchsian and Kleinian groups). Additional topics may include: Geodesic and horocycle flows and their properties, counting closed geodesics and simple closed geodesics, Mostow rigidity, infinite area surfaces.

When Offered Fall.

Prerequisites/Corequisites Prerequisite: Strong performance in undergraduate analysis (e.g., MATH 4130 or MATH 4180) and topology/geometry (e.g., MATH 4530, MATH 4550, or MATH 4560); or permission of instructor.

Comments Offered alternate years.

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