Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.
Explores geodesics on surfaces, focusing on minimizing distances and properties of paths, with examples like great circles on spheres.
Explores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Explores the connected sum of surfaces, focusing on torus and RP2, highlighting the resulting homeomorphism with the sphere.
Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
