Corpus ID: 235593346

# Effective mapping class group dynamics III: Counting filling closed curves on surfaces

@inproceedings{AranaHerrera2021EffectiveMC,
title={Effective mapping class group dynamics III: Counting filling closed curves on surfaces},
author={Francisco Arana-Herrera},
year={2021}
}
We prove a quantitative estimate with a power saving error term for the number of filling closed geodesics of a given topological type and length ≤ L on an arbitrary closed, orientable, negatively curved surface. More generally, we prove estimates of the same kind for the number of free homotopy classes of filling closed curves of a given topological type on a closed, orientable surface whose geometric intersection number with respect to a given filling geodesic current is ≤ L. The proofs rely… Expand
3 Citations

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