MT3542 – Hyperbolic Geometry Hyperbolic Geometry §0 Introduction §1 Background and Motivation §2 Length and Distance in Hyperbolic Geometry §3 Circles and Lines §4 Mobius Transformations and Geodesics in H §5 More on Geodesics §6 Angles and Area in the Upper Half Plane Lectures 1 to 6 Solutions §7 Poincare Disc Model §8 Gauss Bonnet Theorem §9 Right Angled Triangles §10 Sine and Cosine Rules §11 Fixed Points of Mobius Transformations §12 Classifying Mobius Transformations Lecture 7 to 12 Solutions §13 Classifying Mobius Transformations §14 The Displacement Function Introduction to Fushian Groups §15 Fushian Groups §16 Fundamental Domains §17 Dirichlet Polygons Contruction §18 Dirichlet Polygons Examples Lecture 13 to 18 Solutions §19 Generators and Relations §20 Poincares Theorem No Boundary Vertices §21 Poincares Theorem Examples §22 Poincares Theorem Boundary Vertices §23 Final Remarks Lecture 19 to 23 Solutions §24 Revision Related