Hyperbolic Geometry, Fuchsian Groups and Moduli Spaces - Lecture 1

Hyperbolic Geometry, Fuchsian Groups and Moduli Spaces - Lecture 1

Explore the foundations of hyperbolic geometry in this comprehensive lecture from the "Geometry and Topology for Lecturers" workshop. Delve into the upper half-plane model, examining its automorphisms and properties of the hyperbolic metric. Investigate geodesics, completeness, and the unique characteristics of hyperbolic triangles. Compare the disk model and hyperboloid model, uncovering their relationships and distinctions. Engage with hyperbolic trigonometry and gain insights into the constant curvature of hyperbolic space. Perfect for mathematics lecturers and researchers seeking to deepen their understanding of non-Euclidean geometries and their applications in topology and moduli spaces.