RT Web Page DB /z-wcorg/ DS http://worldcat.org ID 743406573 LA English UL http://purl.stanford.edu/ww956ty2392 T1 Geometric transitions from hyperbolic to Ads geometry A1 Danciger, Jeffrey Edward., Kerckhoff, Steve,, Carlsson, G., Mirzakhani, Maryam,, Stanford University., Department of Mathematics., YR 2011 AB We introduce a geometric transition between two homogeneous three-dimensional geometries: hyperbolic geometry and anti de Sitter (AdS) geometry. Given a path of three-dimensional hyperbolic structures that collapse down onto a hyperbolic plane, we describe a method for constructing a natural continuation of this path into AdS structures. In particular, when hyperbolic cone manifolds collapse, the AdS manifolds generated on the "other side" of the transition have tachyon singularities. The method involves the study of a new transitional geometry called half-pipe geometry. We also discuss combinatorial/algebraic tools for constructing transitions using ideal tetrahedra. Using these tools we prove that transitions can always be constructed when the underlying manifold is a punctured torus bundle.