Geometry III/IV
Epiphany 2019
The Michaelmas 2018 webpage
- V. V. Prasolov, Non-Euclidean Geometry (this book was distributed in the class, thanks to the kind permission of the author and the publisher).
- G. Jones, Algebra and Geometry (these lecture notes are available on DUO, thanks to the kind permission of the author).
Who is who |
Preliminary course content (subject to change):
Möbius transformations, hyperbolic geometry, further topics (geometric surfaces, discrete groups).
Schedule:
Week 11: Möbius transformations, inversion.
Week 12: Inversion, Möbius transformations and cross-ratios.
Week 13: Inversion in the space and stereographic projection. Conformal models of hyperbolic geometry (Poincaré
disc).
Week 14: Isometries of Poincaré disc model. Upper half-plane model of hyperbolic geometry.
Week 15: Elementary hyperbolic geometry.
Week 16: Area in hyperbolic geometry. Projective models of hyperbolic geometry: Klein model revisited.
Week 17: Hyperboloid model. Types of isometries of the hyperbolic plane.
Week 18: Isometries and their invariant sets. Horocycles and equidistant curves. Taming infinities with horocycles.
Week 19: Family of geometries: sphere-plane-hyperbolic plane. Discrete groups acting on the hyperbolic plane.
Week 20: Hyperbolic surfaces. Review via 3D hyperbolic geometry.
Problems classes:
Outlines:
4H Reading material: see the description here.
Homeworks: There will be four homework assignments to be handed in on weeks 14, 16, 18, and 20