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 |
| Summary: | 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. |
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| ISSN: | 2050-5094 |