Density of systoles of hyperbolic manifolds
We show that for each $n \ge 2$, the systoles of closed hyperbolic $n$-manifolds form a dense subset of $(0, +\infty )$. We also show that for any $n\ge 2$ and any Salem number $\lambda $, there is a closed arithmetic hyperbolic $n$-manifold of systole $\log (\lambda )$. In particular, the Salem con...
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Académie des sciences
2024-11-01
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| Series: | Comptes Rendus. Mathématique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.689/ |
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| author | Douba, Sami Huang, Junzhi |
| author_facet | Douba, Sami Huang, Junzhi |
| author_sort | Douba, Sami |
| collection | DOAJ |
| description | We show that for each $n \ge 2$, the systoles of closed hyperbolic $n$-manifolds form a dense subset of $(0, +\infty )$. We also show that for any $n\ge 2$ and any Salem number $\lambda $, there is a closed arithmetic hyperbolic $n$-manifold of systole $\log (\lambda )$. In particular, the Salem conjecture holds if and only if the systoles of closed arithmetic hyperbolic manifolds in some (any) dimension fail to be dense in $(0, +\infty )$. |
| format | Article |
| id | doaj-art-031240805258479cbc6c7c2f90f639f1 |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-031240805258479cbc6c7c2f90f639f12025-02-07T11:26:37ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692024-11-01362G121819182410.5802/crmath.68910.5802/crmath.689Density of systoles of hyperbolic manifoldsDouba, Sami0Huang, Junzhi1Institut des Hautes Études Scientifiques, 35 route de Chartres, 91440 Bures-sur-Yvette, FranceDepartment of Mathematics, Yale University, New Haven, CT 06511, USAWe show that for each $n \ge 2$, the systoles of closed hyperbolic $n$-manifolds form a dense subset of $(0, +\infty )$. We also show that for any $n\ge 2$ and any Salem number $\lambda $, there is a closed arithmetic hyperbolic $n$-manifold of systole $\log (\lambda )$. In particular, the Salem conjecture holds if and only if the systoles of closed arithmetic hyperbolic manifolds in some (any) dimension fail to be dense in $(0, +\infty )$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.689/Geometric topologyhyperbolic manifoldssystolesarithmetic groups |
| spellingShingle | Douba, Sami Huang, Junzhi Density of systoles of hyperbolic manifolds Comptes Rendus. Mathématique Geometric topology hyperbolic manifolds systoles arithmetic groups |
| title | Density of systoles of hyperbolic manifolds |
| title_full | Density of systoles of hyperbolic manifolds |
| title_fullStr | Density of systoles of hyperbolic manifolds |
| title_full_unstemmed | Density of systoles of hyperbolic manifolds |
| title_short | Density of systoles of hyperbolic manifolds |
| title_sort | density of systoles of hyperbolic manifolds |
| topic | Geometric topology hyperbolic manifolds systoles arithmetic groups |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.689/ |
| work_keys_str_mv | AT doubasami densityofsystolesofhyperbolicmanifolds AT huangjunzhi densityofsystolesofhyperbolicmanifolds |