Polynomially many surfaces of fixed Euler characteristic in a hyperbolic 3-manifold
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908865339064320 |
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| author | Lackenby, Marc Tsvietkova, Anastasiia |
| author_facet | Lackenby, Marc Tsvietkova, Anastasiia |
| contents | We give an upper bound for the number of compact essential orientable non-isotopic surfaces, with Euler characteristic at least some constant $χ$, properly embedded in a finite-volume hyperbolic 3-manifold $M$, closed or cusped. This bound is a polynomial function of the volume of $M$, with degree that depends linearly on $|χ|$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03716 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Polynomially many surfaces of fixed Euler characteristic in a hyperbolic 3-manifold Lackenby, Marc Tsvietkova, Anastasiia Geometric Topology Differential Geometry 57K32 We give an upper bound for the number of compact essential orientable non-isotopic surfaces, with Euler characteristic at least some constant $χ$, properly embedded in a finite-volume hyperbolic 3-manifold $M$, closed or cusped. This bound is a polynomial function of the volume of $M$, with degree that depends linearly on $|χ|$. |
| title | Polynomially many surfaces of fixed Euler characteristic in a hyperbolic 3-manifold |
| topic | Geometric Topology Differential Geometry 57K32 |
| url | https://arxiv.org/abs/2603.03716 |