Iso-length-spectral Hyperbolic Surface Amalgams
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866908483049226240 |
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| author | Wu, Yandi |
| author_facet | Wu, Yandi |
| contents | Two negatively curved metric spaces are iso-length-spectral if they have the same multisets of lengths of closed geodesics. A well-known paper by Sunada provides a systematic way of constructing iso-length-spectral surfaces that are not isometric. In this paper, we construct examples of iso-length-spectral surface amalgams that are not isometric, generalizing Buser's combinatorial construction of Sunada's surfaces. We find both homeomorphic and non-homeomorphic pairs. Finally, we construct a noncommensurable pair with the same weak length spectrum, the length set without multiplicity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_11752 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Iso-length-spectral Hyperbolic Surface Amalgams Wu, Yandi Geometric Topology Differential Geometry 57K20 Two negatively curved metric spaces are iso-length-spectral if they have the same multisets of lengths of closed geodesics. A well-known paper by Sunada provides a systematic way of constructing iso-length-spectral surfaces that are not isometric. In this paper, we construct examples of iso-length-spectral surface amalgams that are not isometric, generalizing Buser's combinatorial construction of Sunada's surfaces. We find both homeomorphic and non-homeomorphic pairs. Finally, we construct a noncommensurable pair with the same weak length spectrum, the length set without multiplicity. |
| title | Iso-length-spectral Hyperbolic Surface Amalgams |
| topic | Geometric Topology Differential Geometry 57K20 |
| url | https://arxiv.org/abs/2410.11752 |