Arithmetic modular links
Jos\'e Andr\'es Rodr\'iguez Migueles, Tali Pinsky, Jessica S., Purcell
TL;DR
This paper constructs a sequence of geodesics on the modular surface whose lifts produce complements that are arithmetic 3-manifolds, revealing new connections between geometry and number theory.
Contribution
It introduces a novel sequence of geodesics with complements that are arithmetic 3-manifolds, linking modular surface geometry to arithmetic topology.
Findings
Sequence of geodesics constructed on the modular surface
Complements of canonical lifts are arithmetic 3-manifolds
Establishes new links between geometry and number theory
Abstract
We construct a sequence of geodesics on the modular surface such that the complement of the canonical lifts to the unit tangent bundle are arithmetic 3-manifolds.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Geometric Analysis and Curvature Flows