Intersection Number, Length, and Systole on Compact Hyperbolic Surfaces
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866916980666138624 |
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| author | Torkaman, Tina |
| author_facet | Torkaman, Tina |
| contents | The interaction strength I(X) of a compact hyperbolic surface X is the best upper bound for the intersection number of two closed geodesics divided by the product of their lengths. Let $M_g$ be the moduli space of compact hyperbolic surfaces of genus g and sys(X) the length of a shortest closed geodesic on $X \in M_g$. We determine the asymptotic behavior of I(X), as $X \to \infty$ in $M_g$, in terms of sys(X). We also determine the approximate behavior of the minimum of I(X) over $M_g$, as $g \to \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_09249 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Intersection Number, Length, and Systole on Compact Hyperbolic Surfaces Torkaman, Tina Geometric Topology Differential Geometry Metric Geometry 30F45, 32G15 The interaction strength I(X) of a compact hyperbolic surface X is the best upper bound for the intersection number of two closed geodesics divided by the product of their lengths. Let $M_g$ be the moduli space of compact hyperbolic surfaces of genus g and sys(X) the length of a shortest closed geodesic on $X \in M_g$. We determine the asymptotic behavior of I(X), as $X \to \infty$ in $M_g$, in terms of sys(X). We also determine the approximate behavior of the minimum of I(X) over $M_g$, as $g \to \infty$. |
| title | Intersection Number, Length, and Systole on Compact Hyperbolic Surfaces |
| topic | Geometric Topology Differential Geometry Metric Geometry 30F45, 32G15 |
| url | https://arxiv.org/abs/2306.09249 |