## Three-dimensional Orbifolds and Cone-manifolds |

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3-dimensional 3-manifolds 3-orbifold argument assume base boundary bounded branched bundle circle closed collapsing compact complement complete cone angles cone points cone-manifold structure Conjecture consists constant curvature construction contains convergence corresponding cover curve decomposition defined deformation Dehn surgery denote described developing map dimension doubling edge ends Euclidean example Exercise extended fibration finite fixed folded ball follows geodesic geometric structure given gives graph Hence holonomy hyperbolic cone-manifold hyperbolic structure incompressible infinite injectivity radius isometric knot labelled length limit locally manifold Math meridian metric spaces modelled neighbourhood Note obtained orbifold cover Orbifold Theorem orientable original OSFS pieces pillowcase possible proof quotient regular removed representation result rotation satellite knot Seifert fibre space sequence singular locus smooth solid torus spherical standard subset Suppose surface symmetry thick Thurston Tokyo topology tori turnover union University vertex vertices volume