2023/07/18 by Tarik Aougab, Aougab, Tarik, Max Lahn +5
Mathematics · #57K20 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2307.09643
openalex publication_date 2023/07/18 · openalex created_date 2023/07/21 · openalex updated_date 2026/07/28
In this note we prove an effective characterization of when two finite-degree covers of a connected, orientable surface of negative Euler characteristic are isomorphic in terms of which curves have simple elevations, weakening the hypotheses to consider curves with explicitly bounded self-intersection number. As an application we show that for sufficiently large N, the set of unmarked traces associated to simple closed curves in a generically chosen representation to SL(N, R) distinguishes between pairs of non-isomorphic covers.