TL;DR
This paper provides a quantitative analysis of Peter Scott's theorems on surface groups, focusing on their local extended residual finiteness and the embedding of geodesics in finite covers, linking geometric data to algebraic properties.
Contribution
It introduces a quantitative framework for Scott's theorems, connecting geometric features of surfaces to algebraic properties of their fundamental groups.
Findings
Quantified residual finiteness of surface groups.
Established bounds for lifting closed geodesics to embedded loops.
Linked geometric data to algebraic properties of surface groups.
Abstract
We quantify Peter Scott's Theorem that surface groups are locally extended residually finite (LERF) in terms of geometric data. In the process, we will quantify another result by Scott that any closed geodesic in a surface lifts to an embedded loop in a finite cover.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Computational Geometry and Mesh Generation