Hyperbolic GeometryIntroduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
Local Homeomorphisms and CoveringsCovers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.
Fundamental GroupsExplores fundamental groups, homotopy classes, and coverings in connected manifolds.
Mayer-Vietoris SequenceExplores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.
Gaussian Curvature and GeodesicsExplores the derivative of curve lengths, fixed-end deformations, geodesics, surface point typologies, and sphere parametrization.