MATH 6640 - Hyperbolic Geometry

Fall. 4 credits. Student option grading.

Prerequisite: MATH 6510 or permission of instructor.

Staff.

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.

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