PreprintarXiv licencearXiv
A topological version of Huber's theorem
Abstract
Let X be a closed hyperbolic surface. We prove that the number of topological types of primitive closed geodesics of length at most L is asymptotic to 1/|Isom(X)|eL/2L. as L grows. Thus Huber's asymptotic remains unchanged after quotienting by topological type, up to the finite symmetry factor coming from the isometry group of X.
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BibTeX
@misc{basmajian2026topological,
title = {{A topological version of Huber's theorem}},
author = {Ara Basmajian and Hugo Parlier},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02274},
eprint = {2609.02274},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02274},
}
RIS
TY - UNPB
TI - A topological version of Huber's theorem
AU - Ara Basmajian
AU - Hugo Parlier
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02274
UR - https://arxiv.org/abs/2609.02274
AB - Let X be a closed hyperbolic surface. We prove that the number of topological types of primitive closed geodesics of length at most L is asymptotic to 1/|Isom(X)|e^L/2L. as L grows. Thus Huber's asymptotic remains unchanged after quotienting by topological type, up to the finite symmetry factor coming from the isometry group of X.
ER -