Unmarked simple length spectral rigidity for covers
Year: 2025
Type: article
Abstract: We prove that every closed, connected, orientable surface S of negative Euler characteristic admits a pair of finite-degree covers which are length isospectral over S but generically not simple length isospectral over S. To do this, we first characterize when two finite-degree covers of a connected, orientable surface of negative Euler characteristic are isomorphic in terms of which curves have simple elevations. We also construct hyperbolic surfaces X and Y with the same full unmarked length spectrum but so that for each k, the sets of lengths associated to curves with at most k self-intersections differ.
Source: Mathematische Annalen
Authors: Tarik Aougab, Max Lahn, Marissa Loving, Nicholas Miller
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
Funder: National Science Foundation
Awards: Curves, Surfaces, and 3-Manifolds: Geometry, Topology, and Dynamics in the Mapping Class Group and Beyond, Hyperbolic Manifolds, Geodesic Submanifolds, and Rigidity for Rank-1 Lattices, PostDoctoral Research Fellowship, Deformation Spaces of Geometric Structures, Combinatorics in Hyperbolic Geometry and Exporting Teichmuller Theory, Hyperbolic Manifolds, Geodesic Submanifolds, and Rigidity for Rank-1 Lattices
OpenAlex ID: W4407875964