Conjecture that simple geodesics on finite modular covers have transcendental or algebraic endpoints, proved for minimal laminations.
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For each nontrivial two-bridge knot, the surgery slopes admitting non-abelian PSL(2,R) representations with hyperbolic meridian are bounded.
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Transcendence of simple geodesics on finite modular covers
Conjecture that simple geodesics on finite modular covers have transcendental or algebraic endpoints, proved for minimal laminations.