The Anti-de Sitter proof of Thurston's earthquake theorem
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909362271813632 |
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| author | Diaf, Farid Seppi, Andrea |
| author_facet | Diaf, Farid Seppi, Andrea |
| contents | Thurston's earthquake theorem asserts that every orientation-preserving homeomorphism of the circle admits an extension to the hyperbolic plane which is a (left or right) earthquake. The purpose of these notes is to provide a proof of Thurston's earthquake theorem, using the bi-invariant geometry of the Lie group $\mathrm{PSL}(2,\mathbb R)$, which is also called Anti-de Sitter three-space. The involved techniques are elementary, and no background knowledge is assumed apart from some two-dimensional hyperbolic geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_03631 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Anti-de Sitter proof of Thurston's earthquake theorem Diaf, Farid Seppi, Andrea Geometric Topology Differential Geometry Thurston's earthquake theorem asserts that every orientation-preserving homeomorphism of the circle admits an extension to the hyperbolic plane which is a (left or right) earthquake. The purpose of these notes is to provide a proof of Thurston's earthquake theorem, using the bi-invariant geometry of the Lie group $\mathrm{PSL}(2,\mathbb R)$, which is also called Anti-de Sitter three-space. The involved techniques are elementary, and no background knowledge is assumed apart from some two-dimensional hyperbolic geometry. |
| title | The Anti-de Sitter proof of Thurston's earthquake theorem |
| topic | Geometric Topology Differential Geometry |
| url | https://arxiv.org/abs/2306.03631 |