Counting geodesics of given commutator length

Viveka Erlandsson, Juan Souto

Research output: Contribution to journalArticle (Academic Journal)peer-review


Let Σ be a closed hyperbolic surface. We study, for fixed g, the asymptotics of the number of those periodic geodesics in Σ having at most length L and which can be written as the product of g commutators. The basic idea is to reduce these results to being able to count critical realizations of trivalent graphs in Σ. In the appendix, we use the same strategy to give a proof of Huber’s geometric prime number theorem.
Original languageEnglish
Article numbere114
JournalForum of Mathematics, Sigma
Publication statusPublished - 15 Dec 2023

Bibliographical note

Funding Information:
The first author gratefully acknowledges support from EPSRC grant EP/T015926/1 and UiT Aurora Center for Mathematical Structures in Computations (MASCOT).

Publisher Copyright:
© The Author(s), 2023. Published by Cambridge University Press.


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