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Geometric transitions : from hyperbolic to Ads geometry

作者: Jeffrey Edward Danciger; Steve Kerckhoff; G Carlsson; Maryam Mirzakhani; Stanford University. Department of Mathematics.
出版商: 2011.
論文: Thesis (Ph. D.)--Stanford University, 2011.
版本/格式:   碩士/博士論文 : 文獻 : 碩士論文/博士論文 : 電子書   電腦資料 : 英語
資料庫:WorldCat
提要:
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  再讀一些...
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資料類型: 文獻, 碩士論文/博士論文, 網際網路資源
文件類型: 網路資源, 電腦資料
所有的作者/貢獻者: Jeffrey Edward Danciger; Steve Kerckhoff; G Carlsson; Maryam Mirzakhani; Stanford University. Department of Mathematics.
OCLC系統控制編碼: 743406573
注意: Submitted to the Department of Mathematics.
描述: 1 online resource.
責任: Jeffrey Danciger.

摘要:

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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