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Geometric transitions : from hyperbolic to Ads geometry

Auteur : Jeffrey Edward Danciger; Steve Kerckhoff; G Carlsson; Maryam Mirzakhani; Stanford University. Department of Mathematics.
Éditeur: 2011.
Dissertation: Ph. D. Stanford University 2011
Édition/format:   Thèse/dissertation : Document : Thèse/mémoire : Livre électronique   Fichier d'ordinateur : Anglais
Base de données:WorldCat
Résumé:
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  Lire la suite...
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Détails

Type d’ouvrage: Document, Thèse/mémoire, Ressource Internet
Type de document: Ressource Internet, Fichier d'ordinateur
Tous les auteurs / collaborateurs: Jeffrey Edward Danciger; Steve Kerckhoff; G Carlsson; Maryam Mirzakhani; Stanford University. Department of Mathematics.
Numéro OCLC: 743406573
Notes: Submitted to the Department of Mathematics.
Description: 1 online resource
Responsabilité: Jeffrey Danciger.

Résumé:

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.

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Primary Entity

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