Counting geodesics of given commutator length
Let $\Sigma $ be a closed hyperbolic surface. We study, for fixed g, the asymptotics of the number of those periodic geodesics in $\Sigma $ 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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2023-01-01
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| Series: | Forum of Mathematics, Sigma |
| Subjects: | |
| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509423001147/type/journal_article |
| _version_ | 1797390257807687680 |
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| author | Viveka Erlandsson Juan Souto |
| author_facet | Viveka Erlandsson Juan Souto |
| author_sort | Viveka Erlandsson |
| collection | DOAJ |
| description | Let
$\Sigma $
be a closed hyperbolic surface. We study, for fixed g, the asymptotics of the number of those periodic geodesics in
$\Sigma $
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
$\Sigma $
. In the appendix, we use the same strategy to give a proof of Huber’s geometric prime number theorem. |
| first_indexed | 2024-03-08T23:08:08Z |
| format | Article |
| id | doaj.art-0bcb7bf2f0c94eefbf8e6e0c71bc2364 |
| institution | Directory Open Access Journal |
| issn | 2050-5094 |
| language | English |
| last_indexed | 2024-03-08T23:08:08Z |
| publishDate | 2023-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj.art-0bcb7bf2f0c94eefbf8e6e0c71bc23642023-12-15T09:48:18ZengCambridge University PressForum of Mathematics, Sigma2050-50942023-01-011110.1017/fms.2023.114Counting geodesics of given commutator lengthViveka Erlandsson0Juan Souto1School of Mathematics, University of Bristol, Woodland Road, Bristol, BS81UG, UK, and Department of Mathematics and Statistics, UiT The Arctic University of Norway, Norway; E-mail:CNRS, IRMAR - UMR 6625, Université de Rennes, Campus de Beaulieu, Rennes, 35042, France; E-mail:Let $\Sigma $ be a closed hyperbolic surface. We study, for fixed g, the asymptotics of the number of those periodic geodesics in $\Sigma $ 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 $\Sigma $ . In the appendix, we use the same strategy to give a proof of Huber’s geometric prime number theorem.https://www.cambridge.org/core/product/identifier/S2050509423001147/type/journal_article37D4037A17 |
| spellingShingle | Viveka Erlandsson Juan Souto Counting geodesics of given commutator length Forum of Mathematics, Sigma 37D40 37A17 |
| title | Counting geodesics of given commutator length |
| title_full | Counting geodesics of given commutator length |
| title_fullStr | Counting geodesics of given commutator length |
| title_full_unstemmed | Counting geodesics of given commutator length |
| title_short | Counting geodesics of given commutator length |
| title_sort | counting geodesics of given commutator length |
| topic | 37D40 37A17 |
| url | https://www.cambridge.org/core/product/identifier/S2050509423001147/type/journal_article |
| work_keys_str_mv | AT vivekaerlandsson countinggeodesicsofgivencommutatorlength AT juansouto countinggeodesicsofgivencommutatorlength |