Geometric transitions : from hyperbolic to Ads geometry
Abstract/Contents
- Abstract
- 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.
Description
| Type of resource | text |
|---|---|
| Form | electronic; electronic resource; remote |
| Extent | 1 online resource. |
| Publication date | 2011 |
| Issuance | monographic |
| Language | English |
Creators/Contributors
| Associated with | Danciger, Jeffrey Edward |
|---|---|
| Associated with | Stanford University, Department of Mathematics |
| Primary advisor | Kerckhoff, Steve |
| Thesis advisor | Kerckhoff, Steve |
| Thesis advisor | Carlsson, G. (Gunnar), 1952- |
| Thesis advisor | Mirzakhani, Maryam |
| Advisor | Carlsson, G. (Gunnar), 1952- |
| Advisor | Mirzakhani, Maryam |
Subjects
| Genre | Theses |
|---|
Bibliographic information
| Statement of responsibility | Jeffrey Danciger. |
|---|---|
| Note | Submitted to the Department of Mathematics. |
| Thesis | Ph.D. Stanford University 2011 |
| Location | electronic resource |
Access conditions
- Copyright
- © 2011 by Jeffrey Edward Danciger
- License
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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