The infinitesimal and global Thurston geometry of Teichm{ü}ller space
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866929202940346368 |
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| author | Huang, Yi Ohshika, Ken'Ichi Papadopoulos, Athanase |
| author_facet | Huang, Yi Ohshika, Ken'Ichi Papadopoulos, Athanase |
| contents | We undertake a systematic study of the infinitesimal geometry of the Thurston metric, showing that the topology, convex geometry and metric geometry of the tangent and cotangent spheres based at any marked hyperbolic surface representing a point in Teichm{ü}ller space can recover the marking and geometry of this marked surface. We then translate the results concerning the infinitesimal structures to global geometric statements for the Thurston metric, most notably deriving rigidity statements for the Thurston metric analogous to the celebrated Royden theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_13381 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | The infinitesimal and global Thurston geometry of Teichm{ü}ller space Huang, Yi Ohshika, Ken'Ichi Papadopoulos, Athanase Geometric Topology Metric Geometry We undertake a systematic study of the infinitesimal geometry of the Thurston metric, showing that the topology, convex geometry and metric geometry of the tangent and cotangent spheres based at any marked hyperbolic surface representing a point in Teichm{ü}ller space can recover the marking and geometry of this marked surface. We then translate the results concerning the infinitesimal structures to global geometric statements for the Thurston metric, most notably deriving rigidity statements for the Thurston metric analogous to the celebrated Royden theorem. |
| title | The infinitesimal and global Thurston geometry of Teichm{ü}ller space |
| topic | Geometric Topology Metric Geometry |
| url | https://arxiv.org/abs/2111.13381 |