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A note on an effective characterization of covers with an application to higher rank representations

Year: 2024

Type: article

Abstract: 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 \mathrm{SL}_{N}(\mathbb{R}) distinguishes between pairs of non-isomorphic covers.

Source: Groups Geometry and Dynamics

DOI: 10.4171/ggd/836

Authors: Tarik Aougab, Max Lahn, Marissa Loving, Nicholas Miller

Institutions: Haverford College, University of Michigan, University of Wisconsin–Madison, University of Oklahoma

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

OpenAlex ID: W4404184974

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