The genus g Teichmüller space Teich(g) is the space of all marked hyperbolic metrics on a genus g surface , modulo homotopy, or equivalently the space of all conformal structures, modulo biholomorphisms isotopic to the identity. 1,060 more words
Mostow rigidity (or, technically, the special case thereof, for , states that if M and N are two closed (i.e. compact and boundary-less) hyperbolic 3-manifolds, and is a homotopy equivalence. 1,185 more words
A new version of SnapPy, a program for studying the topology and geometry of 3-manifolds, is available. Added features include a census of Platonic manifolds, rigorous computation of cusp translations, and substantial improvements to its link diagram component.