Journal of the London Mathematical Society · 2004 · 27 citations · 0 references
Natural SciencesMathematicsGeometrySurface ScienceTopologyComplex GeometryHyperbolic GeometrySurface StructureCompactness TheoremsComplex SurfacesGeometric Structures On ManifoldsHyperbolic ManifoldsHyperbolic SurfacesRiemann SurfacesSurface Topology
The classification theorem of compact surfaces states that every topological orientable compact surface is homeomorphic to a sphere or to a ‘torus’ of genus g, with g=1,2,…. It is proved in the paper that every hyperbolic Riemann surface except for D\{0} can be decomposed into basic pieces of only a few different types: Y-pieces, funnels and half-disks. As a corollary of this result, the generalization of the classification theorem to non-compact surfaces is obtained.