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Geometric transitions : from hyperbolic to Ads geometry

著者: Jeffrey Edward Danciger; Steve Kerckhoff; G Carlsson; Maryam Mirzakhani; Stanford University. Department of Mathematics.
出版: 2011.
論文: Thesis (Ph. D.)--Stanford University, 2011.
エディション/フォーマット:   学位論文/卒業論文 : Document : Thesis/dissertation : 電子書籍   コンピューターファイル : English
データベース:WorldCat
概要:
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  続きを読む
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資料の種類: Document, Thesis/dissertation, インターネット資料
ドキュメントの種類: インターネットリソース, コンピューターファイル
すべての著者/寄与者: Jeffrey Edward Danciger; Steve Kerckhoff; G Carlsson; Maryam Mirzakhani; Stanford University. Department of Mathematics.
OCLC No.: 743406573
注記: Submitted to the Department of Mathematics.
物理形態: 1 online resource.
責任者: Jeffrey Danciger.

概要:

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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