MATH 6640

Hyperbolic Geometry

Course Description

Course information provided by the Courses of Study 2021-2022.

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, and Lorentzian models. Particular attention will be paid to the cases n=2 and n=3. Hyperbolic structures on surfaces will be parametrized using Teichmüller space, and discrete groups of isometries of hyperbolic space will be discussed. Other possible topics include the topology of hyperbolic manifolds and orbifolds; Mostow rigidity; hyperbolic Dehn filling; deformation theory of Kleinian groups; complex and quaternionic hyperbolic geometry; and convex projective structures on manifolds.

When Offered Fall.

Prerequisites/Corequisites Prerequisite: MATH 6510 or permission of instructor.

View Enrollment Information