Integrated MSc-PhD Program


KSM4E12: Introduction to Hyperbolic Geometry

Topics covered include the Poincare metric on the upper half-space and its geodesics, Möbius transformations on  \mathbb{R}^n, complex Möbius transformations, discontinuous groups, Riemann surfaces, hyperbolic geometry, Fuchsian groups, fundamental domains, finitely generated groups, and universal constraints on Fuchsian groups.

Suggested texts:

          1. Alan F. Beardon, The Geometry of Discrete Groups.
          2. Svetlana Katok, Fuchsian Groups.