Iso-length-spectral Hyperbolic Surface Amalgams
Geometric Topology
2025-08-12 v2 Differential Geometry
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.
Cite
@article{arxiv.2410.11752,
title = {Iso-length-spectral Hyperbolic Surface Amalgams},
author = {Yandi Wu},
journal= {arXiv preprint arXiv:2410.11752},
year = {2025}
}
Comments
18 pages, 12 figures. Minor revisions and expanded exposition. To appear in Groups Geom. Dyn