Lifting curves simply
Gaster, Jonah
Original · EN
We provide linear lower bounds for fρ(L), the smallest integer so that every curve on a fixed hyperbolic surface (S,ρ) of length at most L lifts to a simple curve on a cover of degree at most fρ(L). This bound is independent of hyperbolic structure ρ, and improves on a recent bound of Gupta-Kapovich. When (S,ρ) is without punctures, using work of Patel we conclude asymptotically linear growth of fρ. When (S,ρ) has a puncture, we obtain exponential lower bounds for fρ.
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