Marked length spectrum rigidity from rigidity on subsets
Fuente:
arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866911974860783616 |
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| author | Cantrell, Stephen Reyes, Eduardo |
| author_facet | Cantrell, Stephen Reyes, Eduardo |
| contents | We introduce a new method for studying length spectrum rigidity problems based on a combination of ideas from dynamical systems and geometric group theory. This allows us to compare the marked length spectrum of metrics and distance-like functions coming from various geometric origins. Using our new perspective, we provide concise proofs of well-known length spectrum rigidity results and are able to extend classical results to a variety of new settings. Our methods rely on studying Manhattan curves and a coarse geometric analogue of Teichmüller space equipped with a symmetrized version of the Thurston metric. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_13209 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Marked length spectrum rigidity from rigidity on subsets Cantrell, Stephen Reyes, Eduardo Geometric Topology Group Theory We introduce a new method for studying length spectrum rigidity problems based on a combination of ideas from dynamical systems and geometric group theory. This allows us to compare the marked length spectrum of metrics and distance-like functions coming from various geometric origins. Using our new perspective, we provide concise proofs of well-known length spectrum rigidity results and are able to extend classical results to a variety of new settings. Our methods rely on studying Manhattan curves and a coarse geometric analogue of Teichmüller space equipped with a symmetrized version of the Thurston metric. |
| title | Marked length spectrum rigidity from rigidity on subsets |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2304.13209 |