Hyperbolic GeometryIntroduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.
Fundamental GroupsExplores fundamental groups, homotopy classes, and coverings in connected manifolds.
Spectrum of Hyperbolic SurfacesExplores the spectrum of hyperbolic surfaces, discussing thin C-principle, grad, normalized functions, minimum volume, and embedding properties.
Mayer-Vietoris SequenceExplores the Mayer-Vietoris sequence, exact homomorphisms, embedded spheres, and path-connected spaces.
Analysis III: Third ClassCovers the correction of the simple curve definition and the importance of orientation in mathematical analysis.