Iso-length-spectral Hyperbolic Surface Amalgams

Yandi Wu

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arXiv · 2410.11752

Iso-length-spectral Hyperbolic Surface Amalgams

Yandi Wu

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Abstract

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.

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Yandi Wu. 2024-10-15. Iso-length-spectral Hyperbolic Surface Amalgams. https://arxiv.org/abs/2410.11752

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