2011
Mirzakhani
Maryam
Maryam Mirzakhani
Stanford University. Department of Mathematics.
Carlsson
G.
Gunnar
Gunnar Carlsson
1952
en
2011
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.
743406573
743406573
Geometric transitions : from hyperbolic to Ads geometry
Kerckhoff
Steve
Steve Kerckhoff
2016-08-05
Danciger
Jeffrey Edward
Jeffrey Edward Danciger