MATH 6640

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  • Schedule of Classes - February 16, 2018 10:59AM EST
  • Course Catalog - February 12, 2018 11:18AM EST

MATH 6640
Hyperbolic Geometry

Course information provided by the Courses of Study 2017-2018.

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.

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Syllabi: none

  •   Regular Academic Session. 

  • 4 Credits Stdnt Opt

  • 17199 MATH 6640   LEC 001

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  • 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. Prerequisite: MATH 6510 or permission of instructor.