An Introduction to Hyperbolic Geometry
Student No.:50
Time:【Updated】Mon 15:10-17:00/Wed 13:00-14:50, 2014-10-13~2014-11-19
Instructor:Timothy Marshall  [American University of Sharjah, UAE]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2014-10-13
Ending Date:2014-11-19


The place of Wednesday lecture will be changed to Conference Room 3, Floor 2.


The lecture on Nov 12 will be changed to Nov 15 13:00-14:50, Room 3, Floor 2



This short course gives an introduction to hyperbolic geometry, mostly in 2 dimensions, and to surfaces with a hyperbolic structure. We also study the interplay between the geometry of the hyperbolic plane and complex functions. Topics covered include: Mobius transformations, hyperbolic trigonometry, areas, Fuchsian groups, fundamental regions and hyperbolic surfaces. Time permitting, we will also sample some of the techniques and results of hyperbolic geometry and manifolds in 3-dimensions.


Elementary complex analysis, linear algebra, group theory and
topology (only as much topology as occurs in a basic course in analysis is required)


The main reference is

Gareth A. Jones and David Singerman: Complex functions: an algebraic and geometric viewpoint, Cambridge University Press, 1987


Two other useful references:


Alan F. Beardon: The Geometry of Discrete groups, Spinger, 1983

John Ratcliffe: Foundations of Hyperbolic Manifolds, Springer, 1994